Phase Resistance Feedback Control and … for use Title Phase Resistance Feedback Control and Modeling of Thick SMA Actuators Author(s) 李, 軍鋒 Citation 北海道大学. 博士(工学)

Instructions for use

Title Phase Resistance Feedback Control and Modeling of Thick SMA Actuators

Author(s) 李, 軍鋒

Citation 北海道大学. 博士(工学) 甲第11169号

Issue Date 2013-12-25

DOI 10.14943/doctoral.k11169

Doc URL http://hdl.handle.net/2115/54652

Type theses (doctoral)

File Information Junfeng_Li.pdf

Hokkaido University Collection of Scholarly and Academic Papers : HUSCAP

https://eprints.lib.hokudai.ac.jp/dspace/about.en.jsp

PHASE RESISTANCE FEEDBACK

CONTROL AND MODELING OF

THICK SMA ACTUATORS

DOCTORAL DISSERTATION

JUNFENG LI

DIVISION OF HUMAN MECHANICAL SYSTEM AND DESIGN

GRADUATE SCHOOL OF ENGINEERING

HOKKAIDO UNIVERSITY

DECEMBER, 2013

2

CLAIMS OF ORIGINALITY

i

CLAIMS OF ORIGINALITY

This doctoral thesis contains no material which has been accepted for the award of

any other degree or diploma in any university. To the best of the author's knowledge and

belief, it contains no material previously published or written by another person, except

where due reference is made in the text.

Signature: Junfeng Li

December 2013

ii

CONTENTS

iii

CONTENTS

CLAIMS OF ORIGINALITY ........................................................................................ i

CONTENTS ................................................................................................................ iii

DISSERTATION ABSTRACT .................................................................................... vii

LIST OF FIGURES ..................................................................................................... xi

LIST OF TABLES .................................................................................................... xvii

CHAPTER 1: INTRODUCTION .................................................................................. 1

1.1 Background ..................................................................................................... 1

1.2 Research Objectives and Approach .................................................................. 9

1.3 Outline of Thesis ........................................................................................... 10

CHAPTER 2: NICKEL-TITANIUM SHAPE MEMORY ALLOYS ............................ 11

2.1 Phase Transformation Temperature of SMA .................................................. 13

2.2 Two Different Shape-Memory Effects ........................................................... 14

2.2.1 One-way of SMA.................................................................................... 16

2.2.2 Two-way of SMA ................................................................................... 16

2.2.3 Pseudo-elasticity ..................................................................................... 17

2.3 Micro and Macro Analysis of SMA ............................................................... 18

2.4 SMA Actuators .............................................................................................. 20

2.5 Literature Overview....................................................................................... 23

2.5.1 Modeling of SMA ................................................................................... 23

2.5.2 Controlling of SMA ................................................................................ 30

2.6 Chapter Summary .......................................................................................... 34

CHAPTER 3: LATENCY DURATION INVESTIGATION OF SMA ACTUATOR..... 37

CONTENTS

iv

3.1 Introduction ................................................................................................... 37

3.2 Motivation and Target .................................................................................... 37

3.3 Method .......................................................................................................... 38

3.4 Experimental Setup ....................................................................................... 40

3.5 Results........................................................................................................... 44

3.5.1 Results with Different Ambient Temperature .......................................... 44

3.5.2 Results with Binary Control .................................................................... 47

3.6 Consideration and Discussion ........................................................................ 52

3.7 Chapter Summary .......................................................................................... 56

CHAPTER 4: PHASE RESISTANCE FEEDBACK CONTROL TO ACHIEVE RAPID

RESPONSE SPEED ................................................................................................... 57

4.1 Introduction ................................................................................................... 57


4.3 Method .......................................................................................................... 60

4.3.1 Phase Resistance ..................................................................................... 60

4.3.2 Phase Resistance Feedback Control Method (PRFC) .............................. 62

4.3.3 PID controller ......................................................................................... 64

4.3.4 Experimental Setup ................................................................................. 66

4.4 Results........................................................................................................... 70

4.4.1 Phase Resistance Identification ............................................................... 70

4.4.2 Tuning the PID Parameters ..................................................................... 74

4.4.3 Results with PRFC .................................................................................. 77

4.5 Consideration and Discussion ........................................................................ 81

4.6 Chapter Summary .......................................................................................... 86

CONTENTS

v

CHAPTER 5: IMPROVEMENT OF RESPONSE SPEED USING PHASE

RESISTANCE AND DISPLACEMENT AS FEEDBACK .......................................... 89

5.1 Introduction ................................................................................................... 89


5.3 Method .......................................................................................................... 90

5.3.1 Phase Resistance with Displacement Feedback Control (PRDFC) ........... 90

5.3.2 Control System ....................................................................................... 93

5.4 Results........................................................................................................... 95

5.4.1 Tuning PID Parameters ........................................................................... 95

5.4.2 Results with PRDFC ............................................................................... 98

5.5 Consideration and Discussion ...................................................................... 102

5.6 Chapter Summary ........................................................................................ 105

CHAPTER 6: MODELING OF AN SMA ACTUATOR BASED ON THE LIANG AND

ROGERS MODEL.................................................................................................... 107

6.1 Introduction ................................................................................................. 107

6.2 Motivation and Target .................................................................................. 108

6.3 Method ........................................................................................................ 108

6.3.1 Thermal Model of Heat Transfer and Temperature ................................ 108

6.3.2 Phase Transformation and Mechanical Model ....................................... 111

6.4 Results......................................................................................................... 118

6.5 Consideration and Discussion ...................................................................... 125

6.6 Chapter Summary ........................................................................................ 127

CHAPTER 7: CONCLUSIONS AND FUTURE WORKS ........................................ 129

7.1 Conclusions ................................................................................................. 129

CONTENTS

vi

7.2 Future Works ............................................................................................... 131

ACKNOWLEDGEMENTS ...................................................................................... 133

APPENDIX A ........................................................................................................... 135

a. Binary Control Code with Matlab ................................................................ 135

b. PID Controller Code with Resistance as Feedback ....................................... 137

c. Microcontroller Code .................................................................................. 138

APPENDIX B ........................................................................................................... 143

a. Microcontroller ........................................................................................... 143

b. Power Source, Displacement and Force Sensor ............................................ 144

REFERENCES ......................................................................................................... 149

DISSERTATION ABSTRACT

vii


Title of dissertation submitted for the degree

Phase resistance feedback control and modeling of thick SMA Actuators

Shape memory alloy (SMA) actuators have great potential in niche applications

where space, weight, cost and noise are crucial factors. These applications include

mobile robots, microrobot manipulation, smart structures, and artificial muscles.

Despite many of the advantages, they remain mostly as experimental actuators due to

their perceived slow response speed, low accuracy and controllability. In the past,

research had focused on position and force control of thin SMA wires, because they can

be cooled fast in air and as it is easy to obtain rapid response speed for SMA actuators

in this manner. Due to hysteresis and significant nonlinearities in the behavior of shape

memory alloy actuators, it is difficult to obtain rapid response speed of SMA actuators,

which have limited the application of these actuators, especially for thick SMA wires. In

this thesis, effective control systems are applied to achieve rapid response speed control

of SMA wire actuators.

In this thesis, experimental tests are conducted in chapter 3 to show the existence of

latency duration during the heating and cooling process for thick SMA wires 0.5mm in

diameter. The heating times (5s for SMA1 and 3s for SMA2) are decided to obtain the

latency duration with ‘on-off’ binary control. It is important to avoid overheating of

SMA wires which leads to long latency duration and slow to cool when the power is


viii

turned off. In addition, the experimental results show that the ambient temperature has

an effect on the cooling speed. Therefore, the ambient temperature needs to be stable

when the experiments conducted.

Then, an approach is proposed in chapter 4 to design and control a thick SMA

actuator to achieve rapid response speed control with two connected SMA wires. In the

proposed method, a structure with two connected SMA wires is designed and then the

concept of phase resistance is defined to use it as feedback in the response speed control

system. Phase resistance feedback control (PRFC) minimizes cooling time by

shortening the long latency duration of thick SMA wires. To accurately identify phase

resistances, experiments showed that it is important to determine the major hysteresis

loop. Experimental results that demonstrate the advantages and justify the concepts are

also presented.

Subsequently, another method is proposed in chapter 5, the phase resistance with

displacement feedback control (PRDFC), combing both the phase resistance and

displacement as feedback, minimizes cooling time by shortening the long latency

duration of thick SMA wires. PRDFC using segmented SMA wires shortens the latency

duration of SMA wire, which coordinates with each other to make sure the continuity of

output displacement. Two sets of experiment are tested using the step and ramp signals

as reference input. Experimental results show that rapid response speed is achieved

using this method in comparison with the case in which only displacement is used as

feedback.

In chapter 6, a successful empirical relation is proposed in order to model the major

and minor hysteresis loops of behavior for SMA actuators, which considers the amount

of the austenite fraction transformed at a temperature based on Liang and Rogers model.


ix

Finally, the conclusions of the whole work are described and the future works are

presented in chapter 7.

x

LIST OF FIGURES

xi

LIST OF FIGURES

1-1 The structure and the schematic of bending movement of biomimetic fin [1] .... 2

1-2 Micro-robot fish prototype [1] .......................................................................... 3

1-3 Endoscope actuated by SMA wires [2] ............................................................. 4

1-4 An illustration of the mechanical setup with high voltage [4] ............................ 5

1-5 Strain-temperature characteristics [5] ............................................................... 8

1-6 (i) Peltier sandwich structure; (ii) Photo of experiment setup of SMA actuator

[5] ................................................................................................................... 8

2-1 Schematic of austenite fraction-temperature hysteresis ................................... 14

2-2 Schematic for one way of SMA ...................................................................... 15

2-3 Schematic for two ways of SMA .................................................................... 15

2-4 Schematic of stress VS temperature ................................................................ 17

2-5 Schematic of micro and macro phenomenon of SMA ..................................... 19

2-6 Schematic of different SMA actuators ............................................................ 22

2-7 Play hysteresis operator .................................................................................. 28

2-8 Generalized play hysteresis operator .............................................................. 29

3-1 Schematic of output displacement for SMA wire ............................................ 38

3-2 Schematic of the binary control with latency duration Tcd .............................. 39

3-3 Schematic of experimental setup .................................................................... 40

3-4 SMA wires used in the experiment ................................................................. 41

3-5 SMA wires used in the experiment ................................................................. 42

3-6 (i) Photo of the SMA actuator and (ii) Photo of experimental setup ................ 43

3-7 10s as heating time for SMA .......................................................................... 45

LIST OF FIGURES

xii

3-8 Output displacement for SMA ........................................................................ 46

3-9 Results with different ambient temperature for SMA ...................................... 46

3- 10 Heating time of SMA1 ................................................................................ 48

3- 11 Output displacement of SMA1 in ambient temperature 24°C ....................... 48

3-12 Binary control with latency duration Tcd for SMA1 in ambient temperature

24°C .............................................................................................................. 49

3- 13 Output displacement of SMA2 in ambient temperature 24°C ....................... 50

3-14 Binary control with latency duration Tcd for SMA2 in ambient temperature

24°C .............................................................................................................. 50

3-15 Binary control with different heating voltage for SMA1 in ambient

temperature 24°C........................................................................................... 54

3-16 (i) SMA wires; (ii) Results for SMA 0.15mm in diameter; (iii) Results for

SMA 0.5mm in diameter in ambient temperature 21°C .................................. 55

4-1 An illustration of variable structure control [74] ............................................. 58

4-2 Schematic of the binary control with latency duration Tcd ............................... 59

4-3 Phase transformation resistances VS strain ..................................................... 61

4-4 Schematic for the PRFC method .................................................................... 63

4-5 Output displacement with the PRFC ............................................................... 64

4-6 Block diagram of PRFC ................................................................................. 66

4-7(i) Schematic outline of the experimental setup and (ii) Photo of the

experimental setup ......................................................................................... 67

4-8 Driver circuit .................................................................................................. 68

4-9 Control loop of the experiment ....................................................................... 68

4-10 Results with different cut-off frequency for SMA1 and SMA2 in ambient

LIST OF FIGURES

xiii

temperature 24°C........................................................................................... 69

4-11 Results of resistance with heating time 5s for SMA1 in ambient temperature

24°C .............................................................................................................. 71

4-12 Results of resistance with heating time 3s for SMA2 in ambient temperature

24°C .............................................................................................................. 71

4-13 Major hysteresis loop for SMA1 in ambient temperature 24°C ..................... 72

4-14 Major hysteresis loop for SMA2 in ambient temperature 24°C ..................... 72

4-15 Results with different PID parameters for SMA1 in ambient temperature 24°C

...................................................................................................................... 75

4-16 Results with different PID parameters for SMA2 in ambient temperature 24°C

...................................................................................................................... 76

4-17 Results with PRFC for SMA1 in ambient temperature 24°C ......................... 78

4-18 Results with PRFC for SMA2 in ambient temperature 24°C ......................... 79

4-19 Total output displacement with PRFC in ambient temperature 24°C ............. 80

4-20 Detailed output displacement with two cycles for PRFC in ambient

temperature 24°C........................................................................................... 80

4-21 Results with the PRFC and binary control for SMA1 in ambient temperature

24°C .............................................................................................................. 82

4-22 Results with the PRFC and binary control for SMA2 in ambient temperature

24°C .............................................................................................................. 82

4-23 Binary control with or without resistance calculation in ambient temperature

24°C .............................................................................................................. 84

4-24 Results with the binary control for 5 tests in ambient temperature 24°C ....... 85

5-1 Schematic of step reference for the PRDFC method ....................................... 91

LIST OF FIGURES

xiv

5-2 Schematic of ramp reference for the PRDFC method ..................................... 92

5-3 Block diagram of PRDFC, (i) Displacement feedback control; (ii) Phase

resistance feedback control ............................................................................ 93

5-4 Schematic of the experimental setup for displacement feedback control ......... 94

5-5 Results with different parameters of PI controller in ambient temperature 24°C

...................................................................................................................... 96

5-6 Input voltage for different parameters of PI controller in ambient temperature

24°C .............................................................................................................. 96

5-7 Results of resistance for SMA1 with PRDFC in ambient temperature 24°C;

resistance control: Kp=4000, Ki=0.2 ............................................................... 97

5-8 Results of output displacement for SMA1 with PRDFC in ambient temperature

24°C; resistance control: Kp=4000, Ki=0.2 ..................................................... 98

5-9 Results with PRDFC and traditional method in ambient temperature 24°C;

displacement control: Kp=1000, Ki=0.2; resistance control: Kp=4000, Ki=0.2 . 99

5-10 Results of resistance for SMA2 with PRDFC; displacement control: Kp=1000

and Ki=0.2 ..................................................................................................... 99

5-11 Results with PRDFC and traditional method in ambient temperature 24°C;

displcement control: Kp=1000 and Ki=0.2; resistance control: Kp=4000, Ki=0.2

.................................................................................................................... 100


resistance control: Kp=4000, Ki=0.2 ............................................................. 100


resistance control: Kp=1000, Ki=0.2 ............................................................. 101

5-14 Results with overheating for SMA1 in ambient temperature 24°C;

LIST OF FIGURES

xv

displacement control: Kp=1000 and Ki=0.2; resistance control: Kp=4000 and

Ki=0.2 .......................................................................................................... 104

6-1 Block diagram model of SMA ...................................................................... 109

6-2 Schematic of the input voltage ..................................................................... 110

6-3 Schematic of the output temperature ............................................................ 111

6-4 Schematic of martensite fraction-temperature hysteresis ............................... 112

6-5 Schematic of typical austenite fraction-temperature hysteresis ..................... 115

6-6 Schematic of austenite fraction-temperature hysteresis with modification ..... 115

6-7 Schematic of the input voltage ..................................................................... 119

6-8 Schematic of the displacement VS input voltage .......................................... 121

6-9 Simulated austenite fraction versus time ....................................................... 121

6-10 Simulated austenite fraction versus temperature ......................................... 122

6-11 Curve for fitting the normalized martensite starting temperature ................. 122

6-12 Curve for fitting the martensite starting temperature ................................... 123

6-13 Simulation results of the output displacement VS the input voltage ............ 123

6-14 Plot with experimental and simulated data .................................................. 125

7-1 Block diagram for the compensation based on the inverse model ................. 131

B-1 Microcontroller used in experiment ............................................................. 143

B-2 Power source used in experiment ................................................................. 145

B-3 Displacement sensor used in experiment ...................................................... 146

B-4 Force sensor used in experiment .................................................................. 147

xvi

LIST OF TABLES

xvii

LIST OF TABLES

3-1 Parameters for the experiments....................................................................... 42

3-2 Latency duration with different ambient temperature ...................................... 45

3-3 Latency duration with different heating time for SMA1 .................................. 47

3-4 Latency duration with different heating time for SMA2 .................................. 51

3-5 Heating time and cycle time of SMA wires..................................................... 51

4-1 List of important data in Fig. 4-3 .................................................................... 61

4-2 Transformation resistances parameters ........................................................... 70

4-3 Parameters of the SMA1 and SMA2 ............................................................... 81

6-1 Parameters of the experiments ...................................................................... 119

6-2 Simulation parameters .................................................................................. 124

B-1 Detailed information for microcontroller ..................................................... 144

xviii

CHAPTER 1: INTRODUCTION

1

CHAPTER 1:

INTRODUCTION

1.1 Background

A robot is a mechanical or virtual artificial agent, usually an electro-mechanical

machine that is guided by a computer program or electronic circuitry. Robots can be

autonomous or semi-autonomous. By mimicking a life like appearance or automating

movements, a robot may convey a sense of intelligence or thought of its own. Robots

have replaced humans in the assistance of performing those repetitive and dangerous

tasks which humans prefer not to do, or are unable to do due to size limitations, or even

those such as in outer space or at the bottom of the sea where humans could not survive

the extreme environments. There are many kinds of robots, including mining robots,

military robots, teleoperated robots and so on.

Robotics is the branch of technology that deals with the design, construction,

operation, and application of robots, as well as computer systems for their control,

sensory feedback, and information processing. These technologies deal with automated

machines that can take the place of humans in dangerous environments or

manufacturing processes, or resemble humans in appearance, behavior, and/or cognition.

Many of today’s robots are inspired by nature contributing to the field of bio-inspired

robotics. Actuators are like the “muscles” of a robot, the parts which convert stored

energy into movement. By far the most popular actuators are electric motors that spin a

wheel or gear, and linear actuators that control industrial robots in factories. But there

http://en.wikipedia.org/wiki/Electromechanics

http://en.wikipedia.org/wiki/Electromechanics

http://en.wikipedia.org/wiki/Computer_program

http://en.wikipedia.org/wiki/Electronic_circuit

http://en.wikipedia.org/wiki/Autonomous_robot

http://en.wikipedia.org/wiki/Agency_(philosophy)

http://en.wikipedia.org/wiki/Technology

http://en.wikipedia.org/wiki/Robot

http://en.wikipedia.org/wiki/Bio-inspired_robotics

http://en.wikipedia.org/wiki/Bio-inspired_robotics

http://en.wikipedia.org/wiki/Muscle

http://en.wikipedia.org/wiki/Potential_energy

http://en.wikipedia.org/wiki/Potential_energy


2

are some recent advances in alternative types of actuators, powered by electricity,

chemicals, or compressed air.

An actuator is a type of driving mechanism for moving or controlling a mechanism or

system. It is operated by a source of energy, usually in the form of an electric current,

hydraulic fluid pressure or pneumatic pressure, and converts that energy into some kind

of motion. An actuator is the mechanism by which a control system acts upon an

environment. The control system can be simple (a fixed mechanical or electronic

system), software-based (e.g. a printer driver, robot control system), or a human or other

agent. As control and robotic systems continue to decrease in size and weight, there has

been a continuing trend in technology towards ever-smaller scales for mechanical,

optical as well as electro-mechanical devices. The actuator must therefore undergo

similar miniaturisation in design and construction.

Fig. 1-1 The structure and the schematic of bending movement of biomimetic fin [1]

http://en.wikipedia.org/wiki/Hydraulic_fluid

http://en.wikipedia.org/wiki/Pneumatic


3

Fig. 1-2 Micro-robot fish prototype [1]

Following this trend, factors such as power consumption, work density, costs and

space constraints gain increased importance in the selection of suitable technologies.

However, conventional actuators, including electric motors, pneumatic and hydraulic

actuators, suffer a large reduction in power that they can deliver as they are scaled down

in size and weight. This constraint has led to the emergence and development of novel

actuator technologies such as piezoelectric actuators, electrostatics, magnetostrictive

materials and shape memory alloys (SMA). Wang et al. proposed a fish robot actuated

by Shape Memory alloys [1], Fig. 1-1 and Fig. 1-2 show the details of fish robot.

Shape memory alloys (SMA) are metallic alloys which deform at low temperatures

and return to the original undeformed state when heated to higher temperatures. The

shape memory effect is a consequence of a reversion in the crystalline structure between

the low temperature and high temperature phases, which are respectively called the


4

martensite and the austenite of the SMA. The martensite phase is nonsymmetric and

relatively soft, while the austenite phase is symmetric and relatively hard and has a

much higher Young's Modulus. Heating the SMA can be done via Joule heating, which

is resistively heating the material using electric current. Of all the SMAs that have been

discovered so far, NiTi shape memory alloys, also known as Nitinol, have proven to be

the most flexible and successful in engineering applications. One of the ways SMAs are

commonly used is in the form of wires. Already, SMA have been used in a variety of

actuation applications because of advantages such as excellent power-to-mass ratios,

reliability, and silent actuation, such as endoscope (Fig. 1-3).

Fig. 1-3 Endoscope actuated by SMA wires [2]

Ikuta, Tsukumoto and Hirose proposed a control system for a shape memory alloy

(SMA) servo actuator, and its application to a unique medical tool [2]. It is thought that

the electric resistance value of an SMA can be utilized to monitor the transformation of

the SMA directly. Therefore, an antagonistic transformation control scheme using


5

electric resistance feedback is proposed and is verified by several experiments. The

bending angle of each segment can be controlled individually from outside by using

antagonistic electric resistance feedback without any motion sensors. Featherstone and

Teh proposed a method for improving the speed of actuators based on SMA by

increasing the rate at which an SMA element can safely be heated [3]. The method

consists of measuring the electrical resistance of an SMA element, calculating a

maximum safe heating current as a function of measured resistance, and ensuring that

the actual heating current does not exceed this maximum value. In effect, resistance is

being used as a form of temperature measurement, and the maximum safe heating

current is designed to prevent overheating. Experimental results show a substantial

increase in the maximum velocity attainable by this robot, without any change in the

cooling regime, purely as a result of faster heating.

Fig. 1-4 An illustration of the mechanical setup with high voltage [4]

When the SMA wire is applied in fast moving robots, the response speed of the

actuator is important, especially for robots which need thick SMA wires to provide large

forces. However, thick SMA wires are accompanied by large latency durations which

http://link.springer.com/search?facet-author=%22Roy+Featherstone%22

http://link.springer.com/search?facet-author=%22Yee+Harn+Teh%22


6

slow down the reaction speed of the SMA actuators. Due to the slow speed caused by

hysteresis phenomena in SMA which limits the practical application as actuators, many

researches had focused on improving the response speed of the SMA.

Vollach and Shilo explored the capabilities of a fast one-directional actuation mode

based on one-occasional rapid Joule heating of SMA elements [4]. For this purpose, a

unique experimental system (Fig. 1-4) has been developed that applies a high-voltage

electric pulse to a detwined NiTi wire and measures the resulting displacement due to

the martensite to austenite phase transformation. The research demonstrates the great

potential of SMA for applications that require high speeds and large displacements

one-occasional actuation. However, this method demands maximum current (300 A) to

heat the SMA, which is not practically available for application.

As shown in Fig. 1-5, Selden, Cho and Asada proposed the definition of state

transition threshold temperatures and calculated the latency duration when the

temperature increases from TC to TCH and decreases from TH to THC [5]. In steady of

investigation the relationship between latency duration and phase transformation

temperature of SMA, the relationship the latency duration and output displacement is

investigated in chapter 3.

In addition, a method eliminated the latency duration associated with phase transition

of SMA actuators in proposed. As shown in Fig. 1-6, this control method is

implemented using the Peltier effect thermoelectric devices for selective

segment-by-segment heating and cooling. However, due to thermal conductivity along

the wire, it might be troublesome to regulate adjacent segments at different temperatures.

Then, segments are heated and cooled to extreme temperature. there is heat transfer

between adjacent segments. In addition, one potential limitation to the experimental

http://link.springer.com/search?facet-author=%22S.+Vollach%22

http://link.springer.com/search?facet-author=%22D.+Shilo%22


7

apparatus built with Peltier effect is that segments of a SMA wire may shift to adjacent

units, as the SMA wire shrinks and expands. This may cause some error when an

adjacent segment at a different thermal state is brought to the neighboring segment. The

worst case scenario is that every pair of adjacent segments takes different thermal states.

Another potential limitation is that more energy will be needed to heat SMA since the

Peltier needs to be heated first compared with heating the SMA by Joule heating. At last,

the experimental apparatus is heavy because of many Peltier models in the apparatus.

However, these limitations caused by the Peltier models can be eliminated using

electricity to heat the SMA actuators, which are demonstrated in chapter 4. Theoretically,

both latency durations can be shortened which is demonstrated. However, due to the

electricity is used to heat the SMA wire in this thesis, the latency duration when

temperature increases from martensite finish to austenite start is short compared with

the latency duration when the SMA is cooled by air and temperature decreases from

austenite finish to martensite start. Only the latency duration when temperature

decreases from austenite finish to martensite start is shortened by the proposed method.

Other researches about achieving fast response speed and using resistance as

feedback will be introduced in chapter 4 as well. The detailed information about how to

implement Joule heat to shorten the latency duration during the position control using

phase resistance and displacement as feedback is discussed in chapter 5.


8

Fig. 1-5 Strain-temperature characteristics [5]

Fig. 1-6 (i) Peltier sandwich structure;

(ii) Photo of experiment setup of SMA actuator [5]

(i)

(ii)


9

1.2 Research Objectives and Approach

Due to hysteresis effect and nonlinear relationship, SMA actuators have generally

been considered to be slow, inaccurate and difficult to control continuously. The

primary objective of this research is to demonstrate that more rapid response speed of

SMA actuators can be achieved compared with the conventional method using new

design and implementation of practical and effective control systems.

Two approaches proposed here that have been adopted for achieving rapid response

speed. One is phase resistance feedback control (PRFC), which uses two SMA wires

and the results with PRFC will be compared with that of traditional control method

using only one SMA wire applied in PRFC. The other is phase resistance with

displacement feedback control (PRDFC), which uses two SMA wires as well and the

results with PRDFC will be compared with that of traditional control method using one

SMA wire. The total length of SMA wire used in both experimental tests for the second

approach is the same.

In order to apply the phase resistance as feedback to obtain rapid response speed, a

SMA actuator using two SMA wires which are connected together using insulation joint

to prevent short circuiting is proposed. Then, phase transformation resistances of SMA

wires are identified using experimental data. The critical aspect of the proposed method

is to shorten the latency time caused by hysteresis effect of SMA actuators [5]. The

SMA wires are heated separately to prevent interruption arisen from power. The heating

and cooling processes depends on the phase resistances of both wires. And experimental

tests are conducted to testify the effectiveness of the proposed methods.


10

1.3 Outline of Thesis

This thesis is divided into seven chapters and organized in the following manner.

In chapter 2, some background information on SMAs, including more detailed

descriptions of their phases and the phase transformations, as well as the various

arrangements illustrating how SMAs are used as actuators.

In chapter 3, an experimental setup is built in order to test the latency durations of

SMA wires. Detailed information about the experimental setup is demonstrated and the

results of two SMA wires show whether the latency duration exists during both the

heating and cooling processes and the ambient temperature has an effect on the cooling

speed or not. In addition, a criteria is decided to determine the martensite start

displacement during the cooling process.

In chapter 4 and chapter 5, PRFC and PRDFC are proposed here to achieve rapid

response speed of SMA actuator with two connected SMA wires, respectively. The basic

theory of PRFC and PRDFC are introduced and the control systems of PRFC

demonstrate how they work using phase resistances as feedback. Results with PRFC

and PRDFC are compared with that of binary control and traditional control method.

In addition, in chapter 6, a model is proposed to try to represent the major and minor

hysteresis loops of behavior for SMA actuators. The simulation as well as the

experimental results will be presented and compared.

Finally, in chapter 7, a summary of the research achievements will be provided

together with some discussion of future works

CHAPTER 2: NICKEL-TITANIUM SHAPE MEMORY ALLOYS

11

CHAPTER 2:

NICKEL-TITANIUM SHAPE MEMORY

ALLOYS

In the 1930s, the first reported steps towards the discovery of the shape-memory

effect were taken. According to Otsuka and Wayman, A. Ölander discovered the

pseudoelastic behavior of the Au-Cd alloy in 1932. Greninger and Mooradian (1938)

observed the formation and disappearance of a martensitic phase by decreasing and

increasing the temperature of a Cu-Zn alloy. A decade later, the basic phenomenon of

the memory effect governed by the thermoelastic behavior of the martensite phase was

widely reported by Kurdjumov and Khandros (1949) and also by Chang and Read

(1951).

In 1962-1963, the nickel-titanium alloys were developed by the United States Naval

Ordnance Laboratory and commercialized under the trade name Nitinol (an acronym for

Nickel Titanium Naval Ordnance Laboratories). Their remarkable properties were

discovered by accident. A sample that was bent out of shape many times was presented

at a laboratory management meeting. Muzzey, one of the associate technical directors,

decided to see what would happen if the sample was subjected to heat and held his pipe

lighter underneath it [6]. To everyone's amazement the sample stretched back to its

original shape.

There is another type of SMA, called Magnetic shape-memory alloys (MSMAs). Due

to martensitic phase transformation, MSMAs are ferromagnetic materials which exhibit

large strains under the influence of an applied magnetic field.

http://en.wikipedia.org/wiki/United_States

http://en.wikipedia.org/wiki/Naval_Ordnance_Laboratory

http://en.wikipedia.org/wiki/Naval_Ordnance_Laboratory

http://en.wikipedia.org/wiki/Nitinol

http://en.wikipedia.org/wiki/Shape-memory_alloy#cite_note-6

http://en.wikipedia.org/wiki/Diffusionless_transformations

http://en.wikipedia.org/wiki/Ferromagnetic

http://en.wikipedia.org/wiki/Magnetic_field


12

MSMAs, with near-stoichiometric Ni2MnGa being the most studied example, differ

from other magnetostrictive materials, such as Terfenol-D and Galfenol, as they produce

much larger strains by twinning, sometimes as large as 9%, under relatively low bias

magnetic fields. The mechanism is based on the magnetic anisotropy of the material. As

other SMA which change phase between austenite and martensite with the application

of thermal energy, MSMAs produce a similar phase transformation between martensite

1 and martensite 2 (the two variants). Few models have been developed which describe

the constitutive response of MSMAs. To describe the materials behavior,

thermodynamic modeling is typically used. A shift in the direction of magnetization is

produced when applying a stress to a fully strained element exposed to a bias field

because of the nature of MSMAs. The magnitude of this shift changes according to the

strength of the applied field and material properties. Using Faraday's law of induction,

MSMAs may be used for energy harvesting using a pickup coil, or inductor [7-8].

Shape-memory alloys are typically made by casting, using vacuum arc melting or

induction melting. These are special techniques used to keep impurities in the alloy to a

minimum and ensure the metals are well mixed. The ingot is then hot rolled into longer

sections and then drawn to turn it into wire. The way in which the alloys are “trained”

depends on the properties wanted. The “training” dictates the shape that the alloy will

remember when it is heated. This occurs by heating the alloy so that the dislocations

re-order into stable positions, but not so hot that the material recrystallizes. They are

heated to between 400°C and 500°C for 30 minutes. They are then shaped while hot and

are cooled rapidly by quenching in water or by cooling with air. The manufacturing

equipment can be found in many references, such as [9-10]. Concerning about

manufacturing routes of SMA, in the past, many research had focused on this field

http://en.wikipedia.org/wiki/Ingot

http://en.wikipedia.org/wiki/Hot_rolled

http://en.wikipedia.org/wiki/Wire_drawing

http://en.wikipedia.org/wiki/Dislocation

http://en.wikipedia.org/wiki/Recrystallization_(metallurgy)


13

[11-12].

2.1 Phase Transformation Temperature of SMA

The austenite phase transformations of the alloy can be characterized by four

transformation temperatures:

AST : Austenite start temperature

AFT : Austenite finish temperature

MST : Martensite start temperature

MFT : Martensite finish temperature

The martensite fraction can be used to represent the amount of martensite phase in the

alloy during the heating and cooling processes [13]. As shown in Fig. 2-1, with a

temperature less than MFT , the NiTi alloy consists only of the martensite phase. As the

temperature increases beyond AST , austenite begins to form in the alloy and when the

temperature exceeds AFT , the alloy is primarily in the austenite phase. As the alloy is

cooled, martensite begins to form when the temperature drops below MST , and when the

temperature reaches MFT , the alloy is again fully martensitic.

The transition between the austenite and martensite phases can be characterized by a

wide thermal hysteresis loop, especially for thick SMA wires. The hysteresis varies

according to the alloy system. For example, the temperature hysteresis is generally

between 30°C-50°C for NiTi alloys. During phase transitions between martensite and

austenite, most of the physical properties of SMAs vary, including Young's Modulus,

electrical resistance, heat capacity and thermal conductivity. In the possible range where

both martensite and austenite co-exist, nonlinearities and hysteresis are prominent, and


14

they are influenced by material composition, processing and the number of activated

cycles [14].

Fig. 2-1 Schematic of austenite fraction-temperature hysteresis

2.2 Two Different Shape-Memory Effects

In addition to common shape change effects such as elastic and plastic deformations,

as well as thermal expansion and contraction, SMA also exhibit three shape memory

characteristics. Two common effects are one-way and two-way shape memory. A

schematic of the effects is shown below.

As shown in Fig. 2-2 and Fig. 2-3, the procedures are very similar: starting from

martensite (a), adding a reversible deformation for the one-way effect or severe

deformation with an irreversible amount for the two-way (b), heating the sample (c) and

cooling it again (d).

Temperature

Au

sten

ite

frac

tion

0

100%

TMF TAS TMS TAF

Heating

Cooling


15

Fig. 2-2 Schematic for one way of SMA

Fig. 2-3 Schematic for two ways of SMA

One-way

Two-way

a

b

c

d

a

b

c

d


16

2.2.1 One-way of SMA

NiTi alloys exhibits the Shape Memory Effect (SME) when it is deformed while in

the martensitic phase and then unloaded while still at a temperature below MFT . If it is

subsequently heated above AFT , it will regain its original shape by transforming back

into the parent austenitic phase. When the metal cools again it will remain in the hot

shape, until deformed again. Since martensite variants have been reoriented by stress,

the reversion to austenite produces a large transformation strain having the same

amplitude but the opposite direction with the inelastic strain. With the one-way effect,

cooling from high temperatures does not cause a macroscopic shape change. A

deformation is necessary to create the low-temperature shape. On heating,

transformation starts at AST and is completed at AFT (typically 2°C to 20°C or hotter,

depending on the alloy or the loading conditions). AST is determined by the alloy type

and composition and can vary between -150°C and 200°C.

The above described phenomenon is called one-way shape memory effect (or simply,

shape memory effect) because the shape recovery is achieved only during heating.

2.2.2 Two-way of SMA

The two-way shape memory effect is less pronounced than the one-way effect and

usually requires training. In the shape memory effect discussed above, what is

remembered was the shape of the parent phase only; but, under certain conditions it is

possible to two different shapes: one at low temperatures, and one at the

high-temperature shape. This effect was first called ‘‘the reversible shape memory

effect’’ [15-16], but now it is called two-way shape memory effect.

SMA can be trained to exhibit the two-way effect using two methods, one is

spontaneous load-assisted induction, and the other is external load-assisted induction


17

[17]. However, the shape change obtained is in practice less than that of the one-way

effect.

2.2.3 Pseudo-elasticity

Fig. 2-4 Schematic of stress VS temperature

There is another effect, pseudo-elasticity, also known as ‘super-elastic Effect (SE)’. It

is the shape recovery associated with mechanical loading and unloading of SMAs at

temperatures above AFT and is associated with stress-induced martensitic transformation

and reversal to austenite upon unloading.

The stress dependence of the four transition temperatures can be represented as [18]:

0

T

H

dT

d

r

(2-1)

where is the applied stress; rT is the transformed temperature; H is the

transformation latent heat; T is the temperature and 0 the strain resolved along the

direction of the applied stress.

TMF TMS TAS TAF

Nonlinear

region

Temperature

Str

ess


18

As is shown in Fig. 2-4, the temperatures of AST and AFT are highly nonlinear at

low stress levels. Then, the stress dependence of the transformation temperatures can be

expressed as a generalized temperature, given by [19]:

mcdT

d 1

, or 0TcT m (2-2)

where mc/1 is the stress rate, T is the stress dependent transformation temperature and

0T is the zero stress transformation temperature.

2.3 Micro and Macro Analysis of SMA

Concerning about the SMA, it is necessary to introduce changes of crystal structures

and macro shapes during the heating and cooling processes. Many metals have several

different crystal structures at the same composition, but most metals do not show the

shape memory effect. The special property that allows SMA to revert to their original

shape after heating is that their crystal transformation is fully reversible. In most crystal

transformations, the atoms in the structure will travel through the metal by diffusion,

changing the composition locally, even though the metal as a whole is made of the same

atoms. A reversible transformation does not involve this diffusion of atoms, instead all

the atoms shift at the same time to form a new structure, much in the way a

parallelogram can be made out of a square by pushing on two opposing sides. At

different temperatures, different structures are preferred and when the structure is

cooled through the transition temperature, the martensitic structure forms from the

austenitic phase.


19

Fig. 2-5 Schematic of micro and macro phenomenon of SMA

The unique property of Ni-Ti alloys is shape memory effect, which can be explained

in a rough 2-dimensional approximation of the underlying atomic rearrangements,

including the micro and macro analysis of SMA. As shown in Fig. 2-5, the atomic

lattice is primarily in the martensite phase when the temperature is less than AST . The

length of SMA wire is LL when it is applied external force; as the temperature

exceeds AST , austenite layers begin to form. Then, austenite phase completes when the

temperature exceedsAFT . The atomic lattice is primarily in the austenite phase. The

length of SMA wire is L , which is the original length without applying external force;

as the alloy cools, martensite layers begin to form when the temperature decreases

below MST and the atomic lattice is primarily in the martensite phase when the

L L

L+ L

Austenite

T AFT

Twinned Martensite

T MFT

Detwinned Martensite

T AST

Cooling

Heating

External deformation


20

temperature reachesMFT . The length is practically unchanged and it is the same as in the

austenite phase [20].

2.4 SMA Actuators

SMA is used as actuators because of the following advantages.

SMA actuators offer the highest power-to-weight ratio compared with different types

of actuator technologies [21]. Since An SMA actuator only uses the shape recovery of

the alloy and it can be actuated directly via Joule heating, it does not require any

reduction gear system nor other moving parts, resulting in saving material, production,

maintenance costs and easy miniaturisations of simple actuator systems [22]. In addition,

there is no need for friction mechanisms in SMA actuators, such as reduction gear, it

avoids the production of dust particles, sparks and noise. These properties make SMA

actuators highly attractive for miniature applications. Therefore, it is extremely suitable

for areas, such as microelectronics, biotechnology and medical applications, to apply

SMA as actuators.

SMA have many advantages over traditional actuators, but do suffer from a series of

limitations that may impede practical application [23]. Since SMA actuators are

typically actuated electrically, deactivation typically occurs by free convective heat

transfer to the ambient environment. Consequently, SMA actuation is typically

asymmetric, with a relatively fast actuation time and a slow deactuation time. SMA are

subject to structural fatigue [24-26], which is a failure mode by which cyclic loading

results in the initiation and propagation of a crack. It eventually results in catastrophic

loss of function by fracture. The physics behind this fatigue mode is accumulation of


21

microstructural damage during cyclic loading. In addition, SMA are also subject to

functional fatigue, whereby the SMA do not fail structurally, but, due to a combination

of applied stress, and/or temperature, lose the ability to undergo a reversible phase

transformation. At last, SMA actuators are typically actuated electrically by Joule

heating. If the SMA are used in an environment where the ambient temperature is

uncontrolled, unintentional actuation by ambient heating may occur.

SMA spring SMA wire

SMA wire SMA wire

SMA wire Bias spring

SMA spring Bias spring

(1) (2)

(3)

(4)

(5)

http://en.wikipedia.org/wiki/Joule_heating

http://en.wikipedia.org/wiki/Joule_heating


22

Fig. 2-6 Schematic of different SMA actuators

For SMA actuators, SMA wire or spring is used as actuator in practical application in

order to obtain light and tight manipulators. Because SMA actuators utilize the one-way

effect and can only contract in one direction, it is necessary to provide a biasing force to

pull it back to the original length using a dead weight, a bias spring, or another SMA

element in a differential arrangement. According to [27-28], the primary actuator joint

applications can be divided into ten basic types, as shown in Figure 2-6.

SMA spring SMA spring

Bias spring

SMA spring SMA spring

SMA spring Bias spring

SMA wire

SMA wire

SMA wire

(6)

(7) (8)

(9) (10)


23

2.5 Literature Overview

2.5.1 Modeling of SMA

To simulate the behavior of SMAs and as a control design aid, numerous models are

proposed to represent or explain the characteristics of SMAs, most notably in terms of

their thermomechanical relations and the hysteresis effects. Kuribayashi experimentally

observed the relationship between small variations in the force and strain of an SMA

wire, which can be expressed by the following mathematical model [29].

xbuaf (2-3)

where f , u , and x are the force, voltage, and strain, respectively. a and b are

gain constants. Regarding the static model of Eq. (2-3) as the steady state of a dynamic

system, a dynamic model by adding first order terms for G(s) and H (s) in the Laplace

domain is proposed in the following relationship.

)()()()()( sxsbHsusaGsf (2-4)

A thermomechanical law that governs the stress-strain behavior of the SMA element

was proposed by Tanaka, which is expressed by [30-31]

TD (2-5)

where is the Piola-Kirchhoff stress, is the Green strain, T is the temperature,

and is the martensite ratio. D , , and are respectively the elastic modulus,

the thermoelastic, and the transformation tensor.

The phase transformation is described by exponential functions, including heating

and cooling transformation processes. The ratio of martensite of the cooling process

for austenite to martensite can be given by [32]

0])(exp[1 MMSM bTTa (2-6)


24

where Ma and

Mb are positive material parameters, 0 is the initial volumetric

fraction when phase transformation takes place. For the reverse transformation, from

martensite to austenite, it can be expressed by

])(exp[0 AASA bTTa (2-7)

where Aa and

Ab are positive material parameters.

Based on the Tanaka’s original model, Boyd and Lagoudas rewrite Tanaka’s original

model, for a three-dimensional theory construction [33]. The constants Ma ,

Mb ,Aa , and

Ab are estimated by

MFMS

MTT

a

)10ln(2

, M

MM

C

ab ,

ASAF

ATT

a

)10ln(2

,A

AA

C

ab (2-8)

Liang and Rogers proposed an alternative equation to represent the martensite

fraction based on cosine function [34]. This model was applied to acoustic vibration

control studies and its results show good agreement with experimental data [35-36]. The

model can be given by

2

1)](cos[

2

1 00

M

MFMC

TTA , Heating process (2-9)

where )()( MFMMSM TTCTTC , MC is a material parameter.

1)](cos[2

0 A

ASAC

TTA

Cooling process (2-10)

where )()( ASAAFA TTCTTC ,AC is a material parameter. And the

MA and AA

can be defined by

MFMS

MTT

A

, ASAF

ATT

A

(2-11)

Since an antagonistic arrangement of SMA actuators was used in Grant’ experiment,

a single linear transformation kinetics equation without hysteresis effect which


25

simplifies the model is proposed [37].

AF

AFAS

ASAF

AF

AS

TT

TTTTT

TT

TT

0

1

Heating process (2-12)

Dutta and Ghorbel proposed a differential hysteresis model to represent the SMA

behavior [38]. The operation of the SMA actuator involves different physical

phenomena, such as heat transfer, phase transformation with temperature hysteresis,

stress-strain variations and electrical resistance variation accompanying the phase

transformation. The martensite fraction model of major hysteresis loop is given by

)]2

(1[2

1)()(

/

/''

///

uerfduuguhv u (2-13)

where subscripts + and – denote heating and cooling curves, respectively. / and

/ are constants. g and

g are slops functions which can be given by Duhem

model [39]

0)0(

)))((),(()))((),((

vv

utvtugutvtugv (2-14)

where 2/))(()(

uuu , and g , )( 20 IRCg . )(tu and )(tv are the input and

output.

The slop function of the minor hysteresis loop is given by

)2

)(exp(

2)(

2

/

2

/

/

//

unug i (2-15)

where Ni 1 , /in [0, 1].

The resistance of austenite or martensite phase is given by


26

)()21(4

/2

0

0/ T

d

LR MAMA

(2-16)

)(/ TMA , the electrical resistivity of austenite or martensite phase, can by expressed

by

))(exp()( 321 ambA TTpppT (2-17)

9

02

121 )()](1)[()(

i

i

ambiM TTam

mTerfTqqT (2-18)

where 1p ,

2p , 3p ,1q ,

2q ,1m ,

2m , ambT , and ia ( 9,,0 i ) are constant parameters.

Then, the SMA wire electrical resistance R of major hysteresis loop is given by

MA R

v

R

v

R

//11 (2-19)

Concerning about other models to represent the hysteresis effect of smart material,

Preisach modeling of SMA hysteresis is one of the most successful mathematical

models [40-46].

This model can be considered as an operator which integrates infinite weighted

elementary hysteresis operators over a two dimensional region and it can be expressed

by

ddtvtvHtu T )]([)]([)( (2-20)

where )(tv is the input of hysteresis. )(tu is the output of hysteresis. H is an operator

to transform )(tv to )(tu . is the output of an elementary hysteresis operator

subjected to )(tv . is a density function of variables of and to scale outputs

of relays. T is Preisach plan over hysteresis occurs, which is defined as

vvRT :),( 2 (2-21)

where and denote the increasing and decreasing )(tv , respectively.


27

],[)( vvtv indicates the hysteresis input domain.

Generally, the inverse model is derived and used to obtain accurate position tracking

results in position control system [47]. The inverse Preisach model can be expressed

according to the following algorithm.

For a given output )(u at a time and a known )( tv and )( tu of a

hysteresis, increase or decrease )(tv by steps of idv , ni ,,1 , until calculated output

of the Preisach operator be mostly close to )(u , until

0)(,)(])1()([)(])([

tuudvntvHandundvtvH (2-22)

or

0)(,)(])1()([)(])([

tuudvntvHandundvtvH (2-23)

Therefore, )(tv can be interpolated as

0)(,])1()([])([

])1()([)()(

0)(,])1()([])([

])1()([)()(

)]([)( 1

tudvntvHndvtvH

dvntvHudvtv

tudvntvHndvtvH

dvntvHudvtv

tuHtv

(2-24)

Then, the inverse model is expressed by

)()]]([[)]([)( 1 tutuHHtvHtu (2-25)

Unlike the Preisach model which inverse is obtained numerically, the

Prandtl-Ishlinskii hysteresis model is analytically invertible and therefore can be easily

implemented in the hysteresis nonlinearity control system, such as position tracking

control [48-49]. The operator, as shown in Fig. 2-7, illustrates the Input-output relation

of the classical Prandtl-Ishlinskii hysteresis operator. Suppose that ],0[ TCm is the

space of the piecewise monotone continuous functions and the input ],0[)( TCtu m is


28

monotone on each of the sub-intervals ],[ 1ii tt , where

Tttttt Nii ,,,,0 110 . The output of the classical Prandtl-Ishlinskii

model )(ty can be expressed by

drtuFrpty r

R )]([)()( 0 (2-26)

Fig. 2-7 Play hysteresis operator

where )(rp in an inferable positive density function. r is the positive threshold as

Rrrrrr Nii ,,,,0 110 . ][uFris the classical play hysteresis operator

that is analytically expressed for 1 ii ttt ( 1,,1,0 Ni ) by

))]([),(()]([

)0()0),0(()0]([

irrr

rr

tuFtuftuF

wufuF (2-27)

where ),min(,max),( wruruwufr .

Even though the Prandtl-Ishlinskii model has been applied to characterize hysteresis

u

y


29

effects of different smart actuators [50-52], the shortcomings of the model (limitation on

characterizing the behavior of system with output saturation or asymmetric input-output

loops) is eliminated using an alternative generalized play operator [53-54]. As shown in

Fig. 2-8, an increase in input v causes the output of the generalized operator z to

increase along the curve l , while a decrease in input v causes the output of the

generalized operator z to increase along the curver , resulting in an asymmetric loop.

According to Eq. (2-27), the output of the generalized play hysteresis operator is

analytically expressed for 1 ii ttt ( 1,,1,0 Ni ) as

))]([),(()]([

)0()0),0(()0]([

irrr

rr

tuStugtuS

zuguS (2-28)

here ,,)(min(,)(max),( zruruzug llr The output of the generalized

Prandtl-Ishlinskii model, gy , can be expressed by

)(tyg drtuSrp r

R )]([)(0 (2-29)

Fig. 2-8 Generalized play hysteresis operator

y

u


30

The inverse model based on the generalized Prandtl-Ishlinskii model is also

developed and used as a feedforward compensator for the purpose of mitigating

hysteresis nonlinearities of smart materials [55-60]. The output of the generalized

Prandtl-Ishlinskii inverse model, inversey , is formulated in discrete form as [61-62]

0,)]([)()0(

1

0,)]([)()0(

1

)(

0

^1

0

^1

^

^

ukuFpkup

ukuFpkup

kyN

jr

jl

N

jr

jl

inverse

j

j

(2-30)

,))(( 1

00

^

i

j

ii

j

i

j

jpp

pp 1,,1,0 Ni (2-31)

),(0

^

ij

j

i

ij rrpr

Nj ,,1,0 (2-32)

2.5.2 Controlling of SMA

In the past, a number of methods had been proposed to control SMA actuators. PID

control method is a linear control system that can be used to control SMA actuators.

Asua, Etxebarria and Garcia-Arribas reported that among the linear controllers, PI

with anti-windup has the best results for position control of SMA actuators by the

experimental results [63]. Da Silva proposed a proportional controller which is applied

in active shape control of a flexible beam [64]. Experimental data shows that, in order to

eliminate the steady state error for tracking the step signal, the overshoot and actuator

saturation is unavoidable. In tuning the gains of PID controller for position control of

SMA actuators, for large values of error the proportional gain of the controller should be

large enough to produce sufficient control effort for error compensation. On the other

hand, for small values of error, a large proportional gain will result in overshoot and


31

consequently low performance. Popov et al. proposed a PID controller to control the

SMA actuator while two methods (the Ziegler–Nichols and internal model control

methods) are used to tune the PID controller gains [65]. The simulation results show

that the proposed controller is successful in controlling the displacement of the

transition point position closer to the trailing edge in order to produce a higher laminar

flow region on the airfoil and, therefore, decreases the drag force. Shameli, Alasty and

Salaarieh proposed a PID-P3 controller that adds a proportional cubic term to the

conventional PID controller [66]. They showed that PID-P3 controllers were more

effective than conventional PID controllers for precision position control of a miniature

SMA actuator. Since hysteresis effect of SMA actuator is nonlinear system, it is possible

to develop nonlinear control system to control it. In the literature, it has been shown that

fuzzy logic control is robust in controlling nonlinear systems [67-68]. In the early

1970’s, fuzzy control was first introduced in an attempt to design controllers for systems

that are structurally complicated to model owing to inherent nonlinearities and other

modeling complexities [69]. Cocaud et al. considered fuzzy control of SMA artificial

muscles of a 2 DOF robotic arm [70]. Fuzzy PID controllers have shown good accuracy

and robustness against system nonlinearities and parametric uncertainties. In addition,

PWM controllers are appropriate choices for using as position controllers of SMA

actuators in order to reduce the energy consumption by the actuator. Ma and Song

showed that using pulse width modulation for control of a SMA actuator effectively

saves actuation energy while maintaining the same control accuracy as compared to a

conventional PD controller [71]. They showed that PWM demonstrates robustness to

the external disturbances. Song and Ma proposed an improved PWM technique called

Pulse-Width–Pulse-Frequency (PWPF) modulator which demonstrates that the PD

http://www.sciencedirect.com/science/article/pii/S0957415812000979#b0040






32

controller with PWPF modulation consumes 50% less energy than the one without

modulation [72]. The biomimetic control of an anthropomorphic artificial finger is

presented, which is actuated by three antagonistic SMA muscle pairs that are each

configured in a dual spring-biased configuration and it focuses on the design and

experimental verification of a new fuzzy pulse-width-modulated

proportional-integral-derivative (i.e. fuzzy PWM-PID) controller that is capable of

realizing cocontraction of the SMA muscle pairs, as well as online tuning of the PID

gains to deal with system nonlinearities and parameter uncertainties [73]. To maintain a

desired position of a joint, the corresponding agonistic muscle pairs are cocontracted by

the central nervous system and stiffen the joint. Both numerical and experimental results

show the performance advantage of the cocontracting fuzzy PWM-PID controller over

the original PWM-PID controller.

Furthermore, many researches had worked on nonlinear control aspects of SMA

actuators to solve the hysteresis problem in the past. Grant and Hayward demonstrated a

variable structure controller which is applied to a pair of antagonist actuators [74]. In

this thesis, the feedback switches between the two actuators according to the sign of the

displacement error. In addition, a further improvement was added to compensate for

known gross nonlinearities by modulating the current magnitude in a discrete manner as

a function of the state space position. Therefore, it is possible to realize smooth and

robust control with very little cost in complexity. Due to modeling uncertainty,

nonlinear behavior of the system and classic control methods such as

Proportional-Integral-Derivative control are not able to present fast and accurate

performance, a nonlinear robust control algorithm for accurate positioning of a single

degree of freedom rotary manipulator actuated by SMA based on Variable Structure




33

Control is presented [31]. The model includes nonlinear dynamics of the manipulator, a

constitutive model of SMA, and electrical and heat transfer behavior of SMA wire.

Computer simulation and experimental results for different stabilization and tracking

situations are presented and results show fast, accurate, and robust performance of the

control system. A gain-scheduled controller for an SMA actuator is presented [75]. A

model has been proposed based on concepts from physics in order to achieve accurate

control of an SMA actuator which includes Joules heating-convectional cooling to

explain the dynamics of temperature, Fermi-Dirac statistics to explain the variation of

mole fraction with temperature, and a stress-strain constitutive equation to relate

changes in mole fraction and temperature to changes in stress and strain of the SMA.

Then, this model is applied to develop a gain-scheduled controller to control the strain

in the SMA. Simulation and experimental results show fast and accurate control of the

strain in the SMA actuator.

In the second approach of nonlinear controllers, there are many researches focused on

the inverse model control system to compensate the hysteresis effect of SMA nonlinear

system because of its effectiveness and flexibility. As mentioned above, the inverse

models based on the inverse Preisach model [47] or the generalized Prandtl-Ishlinskii

model [55-60] are also developed and used as a feedforward compensator of smart

materials. Neural networks, which possess properties of nonlinear function mapping and

self-adaptation, have been used to model hysteresis and, in some cases, to compensate

for hysteresis in SMA actuators [76]. In addition, a neural network inverse model and a

sliding-mode based robust feedback controller are used to compensate the SMA

hysteresis phenomenon [77]. Since the inverse model was not exact, three more control

signals (PD controller, feedforward controller, and sliding-mode base robust


34

compensator) were modified to improve the control performance in both open-and

closed-loop fashions. Moreover, it would not be exact if there was a change of load or

working environment because the inverse model was trained offline. Webb and

Lagoudas proposed an adaptive hysteresis model for on-line identification and

closed-loop compensation because of inaccurate model based on off-line identification

[78]. Hysteresis compensation based on the Krasnosel’ skii-Pokrovskii hysteresis

inverse model is also presented [79]. To alleviate the problem of direct temperature

measurements of the SMA wire, an observer based on a simplified thermal model of the

SMA wire that requires only rough estimates of the thermal parameters is implemented.

The reference input must be sufficiently rich in order to update the parameters of the

Krasnosel’ skii-Pokrovskii hysteresis model and therefore cannot be used for step

regulation tracking.

2.6 Chapter Summary

This chapter provides essential background information on shape memory alloys,

including the concept of phase transformation temperature, types of SMA, micro and

macro analysis of SMA, modeling and control methods.

Since SMA have many advantages, it is used in commercial or industrial actuator

applications. However, there remains obstacles in developing SMA actuators, such as

slow speed and the difficulty of accurate position tracking control, as well as energy

inefficiency. In order to model and control SMA actuators, many researches had been

developed in the past. And they are introduced and summarized in this chapter.

This dissertation aims to provide some groundwork on practical control strategies to



35

achieve rapid response speed of SMA actuators. Results and significant work that have

been accumulated during this Ph.D. research will be documented and described in depth

in the following chapters. It is hoped that this thesis will be useful for further research of

SMA, including modeling and control of SMA actuators.


36

CHAPTER 3: LATENCY DURATION INVESTIGATION OF SMA ACTUATOR

37

CHAPTER 3:

LATENCY DURATION INVESTIGATION OF

SMA ACTUATOR

3.1 Introduction

There have been some discussions over the years as to whether shape memory alloys

can respond very quickly. As noted in the literature review of chapter 2, researchers

have attempted to improve upon the controllable speed of SMA actuators. Some of the

results are quite significant, especially in the small or micro-actuator scale [31].

In this chapter, we will investigate the possibility of SMA actuators having very rapid

and detectable responses when subjected heating and cooling. The motivations for this

investigation of SMA will first be explained. In section 3.3 and 3.4, the method and

experimental setup will be described, respectively. The results of the experiments are

presented in section 3.5. Some discussions and conclusions about the results are also

presented in section 3.6 and 3.7, respectively.

3.2 Motivation and Target

In order to reduce the latency duration, it needs to be investigated. The objectives of

the experiments described in this chapter are to determine, firstly, there is hysteresis

effect for SMA wire and the cycle time of different heating time with binary control is

different, and secondly, if the latency duration exists due to the hysteresis effect. As

shown in Fig. 3-1, the output displacement increases from zero to S during heating


38

processes ac when the temperature increases, and decreases from S to zero during

cooling process cf when the temperature decreases. However, the output displacement is

unchangeable during the heating process ab and cooling process cd even though the

temperature of SMA increases and decreases, respectively. The time Tab (from a to b)

and Tcd (from c to d) is latency duration of SMA actuator. In this thesis, only the latency

duration Tcd caused by the nonlinear effect of SMA is investigated. It is useful to find

out if the latency duration in an SMA wire can be produced in order to obtain maximum

output displacement with binary control. The results of this investigation will be

important for SMA control in the following chapters.

Fig. 3-1 Schematic of output displacement for SMA wire

3.3 Method

Hysteresis and significant nonlinearities in the behavior of SMA actuators encumber

effective utilization of these actuators, especially actuators using thick SMA wires

which have long latency duration. Instead of controlling temperatures with a Peltier

a b c f d

Dis

pla

cem

ent S

0

Heating

Cooling

Tcd

Time

Tab


39

device, this thesis uses electricity to heat the SMA wires with ‘on-off’ binary control [4].

As shown in Fig. 3-2, Joule resistive heating causes the SMA actuator to output

displacement which increases from zero during the heating process ac when power is

turned on. The output displacement is steady during ab which is caused by the

hysteresis effect in heating process. When power is turned off, the SMA actuator is

cooled with natural convection and the output displacement reaches zero at f during the

cooling process cf (shown with black line1). Since the output displacement is

unchangeable during cd, the latency duration is Tcd.

Fig. 3-2 Schematic of the binary control with latency duration Tcd

The latency duration caused by hysteresis (Tab and Tcd in Fig.3-2) slows both the

heating and cooling response speed, especially during the phase transformation of a

Time

a b c

S

Dis

pla

cem

ent

Volt

age

0

f d

0

On

Heating

Cooling

Off

Tcd

1


40

thick SMA wire from austenite to martensite. This greatly limits the response of SMA

actuators. The heating time is much shorter than the cooling time when the SMA wire is

heated by a large heating current.

3.4 Experimental Setup

Fig. 3-3 Schematic of experimental setup

In order to obtain the output displacement of SMA wire, the experimental setup is

built shown in Fig. 3-3. The fixed end of the wire is connected to a load cell and the

other end is attached to a bias spring. When the SMA wire is heated to achieve the

austenite length and the electric current is discontinued, the bias spring pulls the SMA

wire back to the martensite length. A reflector (reflecting the laser beam) is connected to

the spring for displacement measurements. As the SMA wire contracts or extends, the

reflector moves forward and backward. Both the data for displacement and force is

received by microcontroller, which will be sent to computer. The controller will

calculate the output voltage to microcontroller which will transform it to PWM to heat


41

the SMA wire. 5V is used as the maximum heating voltage to heat the SMA wire. Power

resistor is used to protect the microcontroller.

For the experiment, thick SMA wire is selected. As shown in Fig. 3-4(i), two same

SMA wires (SMA1 and SMA2, 0.5mm in diameter, 140mm in length) are used in the

following tests to obtain the output displacement suffering to different heating time. The

latency duration of both SMA wires will be tested separately. Fig. 3-4(ii) shows the

length of single SMA wire. As shown in Fig. 3-5, three output voltages are measured for

each SMA wire to obtain the variation of resistance. In order to make sure the maximum

input current is about 2A which can heat the SMA wire to finish the austenite phase,

small resistor (1.1Ω) is added in the driver circuit. The resistance calculation function is

denoted by

)/()( 3221 vvvvRsma (3-1)

where 1v ,

2v , and3v , are the input voltages which will be used in chapter 4 and chapter

5. More detailed information is listed in Table 3-1.

Fig. 3-4 SMA wires used in the experiment

140mm

SMA1 SMA2

(i) (ii)


42

Fig. 3-6 shows the schematic of the experimental setup to test the latency duration

with different heating time for SMA wire. In these tests, two SMA wires with the same

length are tested. In the following chapters, they will be connected together to verify the

proposed method. As shown in Fig. 3-6(i), it is the photo of experimental setup of SMA

actuator outlined in Fig. 3-2; Fig. 3-6(ii) is the photo of experimental setup; the

displacement and force are obtained by a KEYENCE LC-2000 laser displacement meter

and a TEDEA-HUNTLEIGH load cell, respectively.

Fig. 3-5 SMA wires used in the experiment

Table 3-1 Parameters for the experiments

Ambient temperature 24°C SMA diameter 0.5mm

MOSFET K2232 SMA length 140mm

Power supply 5V Spring stiffness 653.3N/m

Microcontroller Arduino Pretension force 3.27N

Power resistor

SMA SMA


43

Fig. 3-6 (i) Photo of the SMA actuator and (ii) Photo of experimental setup

Load cell

Reflector

SMA1 or SMA2

Laser sensor

Bias spring

(i)

(ii)

Laser sensor

SMA structure


44

3.5 Results

3.5.1 Results with Different Ambient Temperature

According to the method mentioned in section 3.3, as shown in Fig. 3-7, ‘on-off’

binary control with 5V is applied to heat the SMA. The SMA is heated from t1=5s to

t2=15s. Fig. 3-8 shows the output displacement with input voltage in Fig. 3-7. It shows

that the output displacement is practically unchangeable from a =5s to b=7.5s. From b

to c1=10s, the output displacement increases from zero to the maximum output

displacement 0.81mm during heating process; from c1 to c=15s, the output

displacement is practically unchangeable even heated which means the SMA1 is

overheated; from c to d=35s, the maximum output displacement is 0.9mm when the

power is turned off; the SMA starts the transformation from austenite to martensite

when output displacement is less than 0.81mm from d. Then, the time Tab =2.5s (from a

to b) and Tcd =20s (from c to d) is latency duration of SMA actuator.

The martensite start displacement (0.81mm) is 90 percent of the maximum output

displacement. When there is no overheating process if the heating time is short, the

output displacement will decline to zero during cooling process, and the 90 percent of

the maximum output displacement can be used as criteria to decide the martensite start

displacement.

Since the temperature of SMA wire is the balance of Joule heat and the heat

dissipation to the ambient environment. Therefore, the ambient temperature will affect

the heating and cooling time. Fig. 3-9 shows the results of different ambient temperature

with input voltage in Fig. 3-7. It clearly shows that the SMA has the similar heating

trajectory with different ambient temperature during the heating process from t1=5s to

t2=15s. With the different ambient temperature, the SMA almost finishes the phase

http://dict.youdao.com/w/trajectory/


45

transformation from martensite to austenite at P=0.81mm during the heating process at

10s; the SMA obtains the same maximum output displacement at Q =0.90mm during

the cooling process as well.

However, compared with other ambient temperature, the SMA extends the fastest

when the ambient temperature is 18°C during the cooling process and starts

transformation from austenite to martensite at d1=31s. More detailed information about

latency duration with different ambient temperature is listed in Table 3-2.

Fig. 3-7 10s as heating time for SMA

Table 3-2 Latency duration with different ambient temperature

Ambient temperature (°C) 24 21 18

Latency duration (s) 20 19 16

0 20 40 600

1

2

3

4

5

6

Time (s)

Volt

age

(V)

t1 t2


46

Fig. 3-8 Output displacement for SMA

Fig. 3-9 Results with different ambient temperature for SMA

0 20 40 60-0.5

0

0.5

1

1.5

0 20 40 60-0.5

0

0.5

1

1.5

21°C

18°C

24°C

P

Time (s)

d1 d

Dis

pla

cem

ent

(mm

)

a c

a c b d c1

Cooling Heating

Time (s)

0.9mm

0.81mm

Q

24°C


47

3.5.2 Results with Binary Control

Here, the latency duration and cycle time with different heating time will be

investigated for both SMA wires in ambient temperature 24°C in the following

experiments. The latency duration of both SMA1 and SMA2 is tested. Fig. 3-10 and Fig.

3-11 show the results of different heating time and output displacement of SMA1,

respectively. It is obvious that different heating time leads to different latency duration.

As shown in Fig. 3-11, when the heating time is 4s, the maximum output displacement

is small, about 0.75mm, and the SMA1 starts transformation from austenite to

martensite at d1=16.6s; when the heating time is larger than 5s, such as 7s, the SMA1

will be overheated, and the SMA1 starts transformation from austenite to martensite at

d2=32s. More detailed information about latency duration is listed in Table 3-3. As

mentioned in section 3.3, the SMA finishes martensite phase when the output

displacement reaches zero. Since there are small offset from the position zero when

SMA1 finishes the phase transformation from austenite to martensite during the cooling

process, a horizontal line along the martensite completion part is used to decide the

martensite finish time. According to this criteria, the SMA1 finishes the martensite

phase at f=55s when the heating time is 4s.

Table 3-3 Latency duration with different heating time for SMA1

Heating time (s) 10 9 8 7 6 5 4

Latency duration (s) 20 18.6 18. 5 17 16 13 7.6

Maximum

Displacement S(mm)

0.9

0.9

0.9

0.9

0.9

0.84 0.75


48

Fig. 3- 10 Heating time of SMA1

Fig. 3- 11 Output displacement of SMA1

in ambient temperature 24°C

0 20 40 600

1

2

3

4

5

6

10 s9 s8 s7 s6 s5 s4 s

0 20 40 60-0.5

-0.3

-0.1

0.1

0.3

0.5

0.7

0.9

1.1

1.3

1.5

10 s9 s8 s7 s6 s5 s4 s

Time (s)

Time (s)

Dis

pla

cem

ent

(mm

)

d1

Offset

Martensite completion

Horizontal line

f d2

Volt

age

(V)


49

In order to prevent from overheating exactly, the heating time 5s is used to obtain

maximum output displacement which is 0.84mm; As shown in Fig. 3-12, the SMA1

starts the phase transformation from austenite to martensite at d =23s when the

martensite start displacement (0.76mm) is 90 percent of the maximum output (0.84mm).

Then the SMA1 finishes the cooling process at f=60s. Fig. 3-13 shows the results of

output displacement with different heating time for SMA2. It is obvious that different

heating time leads to different output displacement as well. Since the maximum output

displacement (0.71mm) during the heating process is almost the same as that during the

cooling process when SMA2 is overheated, the martensite start displacement can not be

decided by percentage of maximum output displacement. Therefore, the latency

duration of SMA2 with different heating time, which is overheated or not, is decided by

the same criteria (90%) as SMA1.

Fig. 3-12 Binary control with latency duration Tcd for SMA1


0 20 40 60-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

a b c

f

d

Tcd

Time (s)

Dis

pla

cem

ent

(mm

)

0.84mm 0.76mm

S


50

Fig. 3- 13 Output displacement of SMA2


Fig. 3-14 Binary control with latency duration Tcd for SMA2


0 20 40 60-0.5

0

0.5

1

1.5

0 20 40 60-0.5

0

0.5

1

1.5

5 s4s3.5 s3 s2.6 s2.3 s

a b c

f

d

Tcd

Time (s)

Time (s)

Dis

pla

cem

ent

(mm

) D

ispla

cem

ent

(mm

)

0.64 mm

0.71mm

S


51

Table 3-4 Latency duration with different heating time for SMA2

Heating time (s) 5 4 3.5 3 2.6 2.3

Latency duration (s) 23 15.5 16 14 10.7 9.9

Maximum

Displacement S(mm)

0.71

0.71

0.71

0.71

0.68 0.64

Fig. 3-13 also shows that when the heating time is 5s, the SMA wire will be

overheated which leads to take longer time to decline when the power is turned off. In

order to prevent overheating exactly, the heating time is set 3s to obtain maximum

output displacement S= 0.71mm for SMA2; when the heating time is 2.3s, the output

displacement is about 0.64mm. More detailed information is listed in Table 3-4.

Fig. 3-14 shows results of the latency duration with heating time 3s for SMA2. The

SMA2 completes the phase transformation from austenite martensite during heating

process ac. And SMA2 completes the phase transformation from martensite to austenite

during cooling process cf. According to the criteria mentioned above, the martensite

start displacement is 0.64mm. The SMA2 starts the martensite phase at d=22s and

finishes the cooling process at f=59s. Comparison about the latency duration

corresponding to Fig. 3-1 is listed in Table 3-5.

Table 3-5 Heating time and cycle time of SMA wires

Tab Tbc Tcd Tdf Cycle time

SMA1 1.8s 3.2s 13s 36s 54s

SMA2 1.7s 1.3s 14s 37s 55s


52

3.6 Consideration and Discussion

The prototype system developed for the experimental investigation of latency

duration has demonstrated the feasibility. There are, however, a few critical points

needing further consideration.

1. As shown in Fig. 3-8, the output displacement slightly changes from a to b and

the minimum output displacement is -0.08mm. In addition, the output

displacement slightly decreases from c1 to c when heated. The reason is when the

temperature of SMA increases, the SMA will expand due to the function that

metals expand when heated and contract when cooled. When the temperature of

SMA is larger than austenite start temperature from b, and when the temperature

of SMA is lower than austenite finish temperature from b to c1, there will be

output displacement caused by the shape memory effect. Compared with the

output displacement caused by shape memory effect, the displacement caused by

thermal expansion can be ignored during bc1. Moreover, the output displacement

slightly increases and the maximum output displacement is 0.9mm during cooling

process cd. The reason is when the temperature of SMA decreases, the SMA will

contract due to the function that metals expand when heated and contract when

cooled. When the temperature of SMA is lower than martensite start temperature

from d, there will be output displacement caused by the shape memory effect and

the displacement caused by thermal contraction can be ignored.

2. As shown in Fig. 3-9, the output displacement is almost the same with different

ambient temperature during the heating process from 5s to 15s. Because heating

voltage is large enough to make the SMA wire finish the phase transformation


53

from martensite to austenite for each test. And the heat loss with different ambient

environment can be ignored during heating process. However, the output

displacement decreases the fastest when the ambient temperature is 18°C, because

the heat loss in 18°C from the SMA to ambient environment is faster than in 22°C

and 24°C. As shown in Table 3-2, the difference of latency duration and cooling

time for different ambient temperature is caused by different heat loss rate in air

[38]. Therefore, in order to obtain correct latency duration, the ambient

temperature should be steady.

3. As shown in Fig. 3-11 and Table 3-5, the latency duration with heating time 10s

(overheated) is 20s which is larger than that with heating time 5s (13s). It takes

much longer time to decline during the cooling process once the SMA is

overheated. Therefore, in order to obtain rapid response speed for SMA actuator,

it is important to control the heating time to avoid overheating.

4. As shown in Fig. 3-12 and Table 3-5, since the heating voltage is large, the

latency duration Tab during the heating process is much smaller compared with

latency duration Tcd. If the heating voltage is small, the latency duration Tab will

be more obviously. As shown in Fig. 3-15, latency duration Tab for input voltage

2.94 V is 4.2s which is larger than with input voltage 5V (1.8s) because the

temperature of SMA increases slower. And, there will be no output displacement

when the input voltage is small, such as 1V because the temperature is less than

martensite start temperature. It is possible to shorten the latency duration Tab with

more segments, such as 4 SMA wires connected together.

5. As shown in Fig.3-12, Fig.3-14, and Table 3-5, due to the specimen error in

length and material, there are small differences about the maximum output


54

displacement (0.84mm for SMA1 and 0.71mm for SMA2) and latency duration

(13s for SMA1 and 14s for SMA2) even though the SMA wires are tested in same

ambient temperature.

6. Fig. 3-16 shows the results with thin SMA wire (0.15mm in diameter) and thick

SMA wire (0.5mm in diameter) with the same maximum output displacement

(0.56mm) and 140mm in length with ambient temperature 21°C, the SMA

finishes the heating process at c and starts the martensite phase at d. Then the

latency durations for both SMA wires are 0.5s and 2s. The output displacement of

both wires reaches zero at 20s and 55s during the cooling process when the power

is turned off, respectively. It clearly shows that the thick SMA wire has longer

latency duration and slower cooling response speed, because it has slower heat

loss ratio than thin one.

Fig. 3-15 Binary control with different heating voltage for SMA1


0 20 40 60-0.5

0

0.5

1

1.5

a b Time (s)

Heating Cooling

5V

1V

2.94V

Dis

pla

cem

ent

(mm

)


55

Fig. 3-16 (i) SMA wires; (ii) Results for SMA 0.15mm in diameter; (iii) Results for

SMA 0.5mm in diameter in ambient temperature 21°C

0 20 40 600

1

2

0 20 40 60

0

0.2

0.4

0.6

0 20 40 600

2

4

6

0 20 40 60

0

0.2

0.4

0.6

Dis

pla

cem

ent

(mm

) V

olt

age

(V)

Time (s)

Dis

pla

cem

ent

(mm

) V

olt

age

(V)

Time (s)

c

d

c d

(iii)

(ii)

(i)

0.5mm 0.15mm


56

3.7 Chapter Summary

The experimental results show that there is hysteresis effect in SMA wire. Due to the

hysteresis effect, it is reasonable to test the latency duration caused by the hysteresis

effect with the binary control.

It has been demonstrated in this chapter that the designed experimental setup can

meet the need of demand to detect the displacement and a 0.5mm diameter NiTi SMA

wire have rapid and detectable responses during the heating process when applied 5V

compared with the cooling process.

Experiments not only indicate the existence of the latency duration at room

temperature which is arisen from the hysteresis effect of SMA wire, but also the

variation of it with different heating time. As shown in Table 3-5, with the proper

heating time to obtain the maximum output displacement and eliminate the overheating,

the latency duration is about 24.1% and 25.4% of cycle time for SMA1 and SMA2,

respectively. We have observed there is small difference between two SMA wires such

as the maximum output displacement.

These observed results are very important to the work in the following chapters.

Based on the results, it is proposed that some new control method may be capable of

improving the speed of response by shortening the latency duration during the cooling

process.


RESPONSE SPEED

57

CHAPTER 4:

PHASE RESISTANCE FEEDBACK CONTROL

TO ACHIEVE RAPID RESPONSE SPEED

4.1 Introduction

Although SMA appears to be attractive for robot applications, they also come with

several limitations. First, since their operating principle is based on a phase transition in

a metal, they have highly nonlinear properties such as the stress-strain relationship,

internal resistance, latent heat of transformation, and thermal conductivity are all phase

dependent. Second, their input-output relations contain a wide hysteresis loop, making

them difficult to control accurately. The third major limitation of SMA is efficiency. The

energy efficiency of SMA is theoretically restricted to approximately 10%. Efficiency is

often less than 1% in practical applications, since the driving principle of the actuator

can be considered as a heat engine operating at low temperatures. Hence, applications of

SMA actuators must be directed at areas where energy efficiency is not a concern. SMA

also have two major inherent mechanical limitations: limited percent strain and low

bandwidth. The absolute percent strain is approximately 8%. With practical applications

restricted to around 5%. The motion bandwidth of SMA actuator is generally low.

Many research had focused on improving the response speed of the SMA, including

antagonistic-pair arrangements [80], variable structures [74], and two-stage relay

control [37]. Thin SMA wires, thinner than 0.2mm, can achieve the aim as actuators

because the cooling speed is fast in air. Thick SMA wires, thicker than 0.5mm, have


RESPONSE SPEED

58

long latency durations, making it difficult to obtain rapid response speeds. Some

researchers have shown that active cooling chips [4, 81] and variable structure control

can improve reaction times of SMA actuators [74] (Fig. 4-1). As a function of

temperature, SMA changes the shape through a metallographic transformation that

results in resistance changes. The relationship between electrical resistance and

displacement of the SMA has been investigated [13]. Resistance also can be used as

feedback in the control system of SMA actuator. SMA actuators are chosen as an

example of a plant with hysteresis and a control system to compensate the hysteresis is

proposed controlling the electrical resistance of SMA, which reflects its state, and the

usefulness of the controller is confirmed experimentally [82].

Fig. 4-1 An illustration of variable structure control [74]


RESPONSE SPEED

59

In chapter 3, the latency duration of SMA wire is investigated. In this chapter, we will

investigate the possibility of SMA actuators having rapid response when using phase

resistance as feedback to shorten the latency duration. The motivations will first be

explained. In section 4.3 and 4.4, the method and results will be described, respectively.

Some discussions and conclusions about the results are also presented in section 4.5 and

4.6, respectively.


Fig. 4-2 Schematic of the binary control with latency duration Tcd

To obtain rapid response speed for SMA actuator, an alternative approach, PRFC

(Phase resistance feedback control), is proposed to control the phase resistance in a

closed-loop feedback system of two connected thick SMA wires. There are two basic

Time a b c

S

Dis

pla

cem

ent

Volt

age

0

f d

0

On

Heating

Cooling

Off

Tcd

e

1


RESPONSE SPEED

60

concepts underlying the PRFC. One is the introduction of phase resistances which

divide the hysteresis loop into four parts. The other is to utilize the phase resistances as

the feedback to reduce the latency duration. Experiments to prove the effectiveness

demonstrated that the latency duration caused by the hysteresis effect was shortened and

showed the advantages of the proposed method. Experimental results that demonstrate

the advantages and justify the concepts are also presented. As discussed in chapter 3, the

traditional control method for position is an ‘on-off’ binary control. As shown in Fig.

4-2, Tcd is the latency duration which has been investigated in chapter 3. Here, PRFC is

proposed to achieve rapid response speeds, like the dotted line 1 (Fig. 4-2). The Joule

resistive heating causes the SMA actuator to contract during the heating process ac

when power is turned on. The SMA actuator is cooled with natural convection which

extends from c and completes the cooling process at e, shortening the latency time Tcd.

4.3 Method

4.3.1 Phase Resistance

The SMA may be seen as a smart material that changes shape due to changes in

temperature. These changes are reversible. The shape memory effect arises from

temperature and stress dependent shifts in the crystalline structure of the SMA, shifts

between martensite and austenite phases. During the phase transformation processes, the

resistance changes with changes in temperature. As with the strain-to-temperature or

resistance-to-temperature relationship, the strain-to-resistance curve exhibits a

hysteresis loop [83-85]. As shown in Fig. 4-3 and Table 4-1, there are four phase

transformation resistances Ras, Raf, Rms, and Rmf. In the heating process, from A to B, the

resistance increases from Rmf to Ras without changes in the output strain; from B to C,


RESPONSE SPEED

61

the resistance decreases from Ras to Raf as the SMA transforms from martensite to

austenite. In the cooling process, from C to D, the resistance decreases from Raf to Rms

without changes in the output strain, while from D to A, the resistance increases from

Rms to Rmf as the SMA transforms from austenite to martensite.

Table 4-1 List of important data in Fig. 4-3

Ras Austenite start resistance

Raf Austenite finish resistance

Rms Martensite start resistance

Rmf Martensite finish resistance

Tab Heating time from A to B

Tbc Heating time from B to C

Tcd Cooling time from C to D

Tdf Cooling time from D to A

Fig. 4-3 Phase transformation resistances VS strain

Mar

tensi

te

Tab

Au

sten

ite

0

100%

Rms Raf Rmf Ras

B A

Tcd

C D

Tbc

Heating

Tdf

Cooling

Resistance

100%

0


RESPONSE SPEED

62

4.3.2 Phase Resistance Feedback Control Method (PRFC)

As shown in Fig. 4-3, we have divided the heating and cooling process into four parts

with times Tab, Tbc, Tcd, and Tdf, as listed in Table 4-1, and a cycle time T is defined as

T=Tab+Tbc+Tcd+Tdf (4-1)

The SMA shrinks during the time Tbc rather than Tab in the heating process and

extends during the time Tdf rather than Tcd in the cooling process. If the gap between the

heating and cooling lines (Fig. 4-3) is large, then the resistance-phase state

characteristics of SMA have strong hysteresis properties. In this case it is simple to

identify phase resistances.

The critical aspect of the PRFC method is to shorten the total cooling time by

controlling the phase resistances with two connected SMA wires (SMA1 and SMA2 in

Fig. 3-4) that are coordinated. Fig. 4-4 shows the basic theory behind this method, using

the definitions in Table 4-1, and may be explained as follows.

As shown in Fig. 4-4(i), in section AC, the resistance of SMA1 is maintained at Rms,

and there is no displacement output from the SMA1 wire. The resistance of SMA2

increases from Rmf to Ras and then decreases to Raf. The SMA2 wire completes the phase

transformation from martensite to austenite. As shown in Fig. 4-4(ii), the SMA2

elongates and then contracts, which respectively leads to positive and negative

displacements during the heating process AC; the maximum output displacement is at S.

The heating time Th can be described by

Th=TAB+TBC=Tab+Tbc (4-2)

In section CD, once the resistance of SMA2 reaches Raf, the SMA1 is rapidly cooled

without any current and the resistance of SMA2 is maintained at Rms. The result is that

there is no displacement output from the SMA2 wire. The resistance of SMA1 increases


RESPONSE SPEED

63

to Rmf and the SMA1 wire completes the phase transformation from austenite to

martensite. During the cooling process, CD, the displacement of SMA1 is positive. The

cooling time Tc can be given as follows

Tc =TCD=Tdf (4-3)

In addition, the time of a cycle for one SMA wire Tsingle is longer than with the binary

control method. It is expressed as follows

Tsingle=Tab+Tbc+TCE+Tdf (4-4)

where TCE > Tcd

Combining the two SMA wires, the latency time Tcd can be eliminated. Therefore the

time of a cycle in PRFC, Tp, is given as

Tp=Th+Tc= Tab+Tbc+Tdf (4-5)

Fig. 4-4 Schematic for the PRFC method

B D E C A Time

Raf

Rms

Ras Rmf

Dis

pla

cem

ent

SMA2

SMA1

Res

ista

nce

0

0

Tab

S

(i)

(ii)

Tbc Tdf Tbc Tab


RESPONSE SPEED

64

Fig. 4-5 Output displacement with the PRFC

To explain the PRFC method in more detail, the output displacement of SMA actuator

is demonstrated. As shown in Fig. 4-5, the displacement is zero when both SMA wires

are in the martensite phase before the PRFC.

Step 1: at the beginning of PRFC, SMA1 is in the martensite starting phase and

SMA2 is in the martensite finishing phase, the output displacement is S.

Step 2: SMA1 is in the martensite starting phase and SMA2 completes the

transformation from martensite to austenite, the output displacement is S as well.

Step 3: once the SMA2 completes the transformation from martensite to austenite,

SMA1 starts the transformation from austenite to martensite. At the same time, SMA2

remains at martensite starting phase, the output displacement is S; Combining the two

SMA wires, Tcd is shortened and the maximum output displacement from step 1 to step

3 is S.

4.3.3 PID controller

The phase resistance Rms needs to be used as feedback to maintain the output

displacement precisely by tuning the PID parameters. A proportional-integral-derivative

controller (PID controller) is a generic control loop feedback mechanism (controller)

widely used in industrial control systems. A PID controller calculates an "error" value as

SMA1 SMA2 Martensite

finish phase

Step 1

Step 2

Step 3

S

+ - + -

S

0 0

http://en.wikipedia.org/wiki/Control_loop

http://en.wikipedia.org/wiki/Feedback_mechanism

http://en.wikipedia.org/wiki/Controller_(control_theory)

http://en.wikipedia.org/wiki/Industrial_control_system


RESPONSE SPEED

65

the difference between a measured process variable and a desired setpoint. The

controller attempts to minimize the error by adjusting the process control inputs. The

PID controller calculation algorithm involves three separate constant parameters, and is

accordingly sometimes called three-term control: the proportional, the integral and

derivative values, denoted P, I, and D, these values can be interpreted in terms of time. P

depends on the present error, I on the accumulation of past errors, and D is a prediction

of future errors, based on current rate of change. The weighted sum of these three

actions is used to adjust the process via a control element such as the position of a

control valve, a damper, or the power supplied to a heating element. By tuning the three

parameters in the PID controller algorithm, the controller can provide control action

designed for specific process requirements. The response of the controller can be

described in terms of the responsiveness of the controller to an error, the degree to

which the controller overshoots the setpoint, and the degree of system oscillation. Note

that the use of the PID algorithm for control does not guarantee optimal control of the

system or system stability. To be able to use the phase resistances as feedback, a PID

controller was installed instead of the traditional ‘on-off’ binary control, and this is

shown in Fig. 4-6. The parameters of the PID controller are based on the value of the

error e. The PWM value is then converted to voltage and heats. Since the

microcontroller can only receive the value from 0 to 255, then the output of PID

controller is converted to this range. The output voltage is from 0 to 5V, and the

following equations represent the error output voltage relationship.

]0,255[,)(

)()( 0 Piddt

tdeKdtteKteKPid d

t

ip (4-6)

where e(t) is the signal error of the resistance.

http://en.wikipedia.org/wiki/Process_variable

http://en.wikipedia.org/wiki/Setpoint_(control_system)

http://en.wikipedia.org/wiki/Algorithm

http://en.wikipedia.org/wiki/Proportionality_(mathematics)

http://en.wikipedia.org/wiki/Integral

http://en.wikipedia.org/wiki/Derivative

http://en.wikipedia.org/wiki/Control_valve

http://en.wikipedia.org/wiki/Damper_(flow)

http://en.wikipedia.org/wiki/Overshoot_(signal)

http://en.wikipedia.org/wiki/Optimal_control


RESPONSE SPEED

66

255/*5 PidVoutput (4-7)

There are two purposes of using resistance as feedback.

1. It can maintain the output displacement without using displacement as feedback.

2. The SMA wire is ready to cool down quickly without duration during the cooling

process since the latency duration is shortened.

Fig. 4-6 Block diagram of PRFC

4.3.4 Experimental Setup

An experimental setup of the proposed double SMA actuator was made, and as

shown in Fig. 4-7(i), SMA wires are connected by an insulation joint to prevent short

circuiting; the fixed end of the wire at the joint is connected to a load cell and the other

is attached to a bias spring. A reflector is connected to the spring for displacement

measurements. As the SMA wire shrinks and extends, the reflection sheet moves

forward and backward. Fig. 4-7(ii) is the experimental setup explained in Fig. 4-7(i).

Detailed parameters of the experiment are shown in Table 3-1.


RESPONSE SPEED

67

(i)

(ii)

Fig. 4-7(i) Schematic outline of the experimental setup and (ii) Photo of the

experimental setup

Reflector

Laser sensor

Load cell

Power

SMA1 SMA2

Bias spring

Insulation joint

Load cell Insulation joint

Reflector

SMA1 SMA

2

Laser sensor

Bias spring


RESPONSE SPEED

68

Fig. 4-8 Driver circuit

Fig. 4-9 Control loop of the experiment


RESPONSE SPEED

69

Fig. 4-10 Results with different cut-off frequency for SMA1 and SMA2


In order to measure the resistance of both SMA wires, the driver circuit is designed

shown in Fig. 4-8. Two SMA wires are measured and the calculation equation can be

expressed by Eq. (3-1) in chapter 3. The displacement is detected as the same in chapter

3 by microcontroller. As shown in Fig. 4-9, a computer is connected to a microcontroller

with a USB port. The microcontroller sends data used as the feedback to the computer

and receives the control values sent by the computer. Then, the microcontroller sends a

PWM value to the driver circuit to control the input voltage of the SMA wires. Before

identify the phase resistance, we need to filter the data obtained from microcontroller.

The sampling time is 0.05s, and to filter out the high-frequency noise component, a

third order Butterworth filter with a cut-off frequency. Fig. 4-10 shows the results with

different cut-off frequency and Wc=2Hz is used in the experiment.

0 20 40 60 80 1001.4

1.45

1.5

1.55

1.6

Without filterWc=5 HzWc=2 Hz

Time (s)

Res

ista

nce

(Ω

)


RESPONSE SPEED

70

4.4 Results

4.4.1 Phase Resistance Identification

To identify phase transformation resistances, it is necessary to determine the major

hysteresis loop of the displacement-to-resistance of SMA wires involved, and it is also

important to determine the heating time, especially to prevent overheating.

In chapter 3, the heating time 5s is used to heat the SMA wire to obtain maximum

output displacement instead of overheating. Fig. 4-11 shows the results of resistance

with heating time 5s in binary control for SMA1. It obviously shows that the resistance

will increase first and then decrease during the heating process. When the power is

turned off, the resistance increases from t3=10s during the cooling process. Fig. 4-12

shows results of resistance with heating time 3s in binary control for SMA2 and the

resistance increases from t3=8s during the cooling process. It obviously shows the same

results as SMA1. Therefore, the hysteresis loop with heating time 5s and 3s are used as

major hysteresis loop to identify the phase resistance of SMA1 and SMA2, respectively.

Table 4- 2 Transformation resistances parameters

Resistances

of SMA1

Ras 1.535Ω

Resistances

of SMA2

Ras 1.445Ω

Raf 1.480Ω Raf 1.390Ω

Rms 1.470Ω Rms 1.360Ω

Rmf 1.515Ω Rmf 1.413Ω

Displacement

of SMA1

Max 0.84mm Displacement

of SMA2

Max 0.71mm

Min -0.08mm Min -0.02mm


RESPONSE SPEED

71

Fig. 4-11 Results of resistance with heating time 5s for SMA1


Fig. 4-12 Results of resistance with heating time 3s for SMA2


0 20 40 601.3

1.4

1.5

1.6

1.65

0 20 40 601.3

1.4

1.5

1.6

1.65

Time (s)

Res

ista

nce

(Ω

)

Time (s)

Res

ista

nce

(Ω

)

Cooling

Heating

Cooling

Heating

t3

t3


RESPONSE SPEED

72

Fig. 4-13 Major hysteresis loop for SMA1 in ambient temperature 24°C

Fig. 4-14 Major hysteresis loop for SMA2 in ambient temperature 24°C

1.4 1.45 1.5-0.2

0

0.2

0.4

0.6

0.8

1.3 1.35 1.4 1.45 1.5-0.2

0

0.2

0.4

0.6

0.8

Resistance (Ω)

A

Cooling

D C

B

Heating

Dis

pla

cem

ent

(mm

)

Rms Raf Rmf Ras

Resistance (Ω)

A

Cooling

D

C

B

Heating

Dis

pla

cem

ent

(mm

)

Rms Raf Rmf Ras


RESPONSE SPEED

73

Fig. 4-13 and Fig. 4-14 show the phase resistance of major hysteresis loop of

SMA1and SMA2, respectively. In segment AB, the SMA wires extend quickly and

complete the phase resistances transformation from Rmf to Ras; in segment BC, the SMA

wires shrink and the resistances decrease from Ras to Raf; in segment CD, the resistances

decrease from Raf to Rms and the SMA wires cool but the output displacements remain

practically unchanged; According to the criteria mentioned in chapter 3, the resistance

decreases from Raf to Rms with 10% declines in the output strain. In segment DA when

the output displacements are less than 0.76mm and 0.64mm, the SMA wires start the

transformation from austenite to martensite for SMA1 and SMA2 at D, respectively.

More detailed information about the transformation resistances of SMA1 and SMA2 is

shown in Table 4-2.


RESPONSE SPEED

74

4.4.2 Tuning the PID Parameters

The PRFC is proposed here to improve on the slow response speed obtained with

binary control. Fig. 4-6 shows the control arrangement of the PRFC where the

resistance coordinator sends the phase resistance as input to SMA1 and SMA2. The PID

controller should be tuned first to obtain proper parameters in the feedback control.

Fig. 4-15(i) shows the results of PID control using resistance as feedback to maintain

the resistance of SMA1 at Rms. When Kp=500, Ki=0, and Kd=0, the resistance increases

quickly since the input voltage which is used to heat and maintain the SMA wire is not

enough. As shown in Fig. 4-15(ii), this results in the output displacement decreasing

quickly without any maintaining; when Kp=4000, Ki=1, and Kd=0, the output

displacement is unstable because Ki=1 is too large and SMA is overheated, the

resistance cannot be maintained at Rms; when Kp=4000, Ki=0.5, and Kd=0, the resistance

can be maintained at Rms from 38s to 50s and there is no steady-state error e. However,

the output displacement (Fig. 4-15(ii)) is maintained at 0.83mm and there is long

latency duration Tm=12s; when Kp=4000, Ki=0.2, and Kd=0, the resistance is maintained

at Rms and the output displacement is maintained around 0.76mm from 23s to 50s even

if there is small steady-state error e. When the power is turned off from 50s, the output

displacement declines quickly. Therefore, Kp=4000, Ki=0.2, and Kd=0, are selected as

the parameters in the PID control. In addition, the PI control can meet the need in the

experiment. Therefore, parameter Kd is set to be zero in the PID controller.

According to the same method, the parameters for SMA2 are tuned. Fig. 4-16(i) and

Fig. 4-16(ii) show the results of PID control using resistance as feedback and output

displacement, respectively. It clearly shows that Kp=4000, Ki=0.18, and Kd=0, are the

suitable parameters to maintain the output displacement at 0.64mm.


RESPONSE SPEED

75

Fig. 4-15 Results with different PID parameters for SMA1


0 20 40 60 80-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 20 40 60 801.2

1.3

1.4

1.5

1.6

1.7

kp=4000, ki=0.1, kd=0kp=500, ki=0, kd=0kp=4000, ki=0.2, kd=0kp=4000, ki=1, kd=0kp=4000, ki=0.5, kd=0Reference

40 45 50 551.441.461.481.5

1.52

e

Time (s)

Res

ista

nce

(Ω

)

Time (s)

Dis

pla

cem

ent

(mm

)

Maintaining

Maintaining

(i)

(ii)

Tn

Tm


RESPONSE SPEED

76

Fig. 4-16 Results with different PID parameters for SMA2


0 20 40 60 801.2

1.25

1.3

1.35

1.4

1.45

1.5

1.55

1.6

Referencekp=4000, ki=0.18, kd=0kp=4000, ki=1, kd=0kp=500, ki=0, kd=0

0 20 40 60 80 100

0

2

4

6

0 20 40 60 80 1001.2

1.25

1.3

1.35

1.4

1.45

1.5

1.55

1.6

0 20 40 60 80

-0.2

0

0.2

0.4

0.6

0.8

kp=4000, ki=1, kd=0kp=4000, ki=0.18, kd=0kp=500, ki=0, kd=0

Res

ista

nce

(Ω

) D

ispla

cem

ent

(mm

)

Time (s)

Maintaining

Maintaining

Time (s)

(i)

(ii)


RESPONSE SPEED

77

4.4.3 Results with PRFC

The two SMA wires will be actuated separately, using these parameters to test the

possibility of obtaining the results discussed in Fig. 4-4. Fig. 4-17 shows the results with

PRFC for SMA1 when the power for SMA2 is turned off. Fig. 4-17(i) shows, in the

heating process, the input voltage is Vh which can make a maximum output

displacement without overheating. In the maintaining process, the resistance is

maintained at Rms using resistance as feedback. Fig. 4-17(iii) shows the results of output

displacement. It clearly shows the heating, maintaining, and cooling processes and the

output displacement is maintained successfully during the maintaining section. Fig.

4-18 shows the results with PRFC for SMA2 when the power for SMA2 is turned off.

Fig. 4-18(i) shows that the input voltage is 5V and the heating time is 3s to obtain a

maximum output displacement during the heating process. Fig. 4-18(iii) shows the

results of output displacement of SMA2. During the maintaining section, the output

displacement is maintained at 0.64mm from 123s to 185s successfully.

With the results of SMA wires actuated separately, the two SMA wires will be

actuated together to demonstrate the results of rapid response speed with PRFC. Fig.

4-17(ii) and Fig. 4-18(ii) are plots of the variations of the actual resistances of SMA1

and SMA 2 using the phase resistances as the feedback. And the resistance is maintained

at Rms successfully. When the resistance of SMA2 reaches Raf at C=123s, SMA1 cools

quickly from the phase resistance Rms; then when the resistance of SMA1 reaches Raf at

E=185s, SMA2 cools quickly from the phase resistance Rms; during CE, there is no

output displacement though the resistances of SMA2 increase from Raf to Rms. The

latency duration of the cooling process is shortened, combining the heating process AC

of SMA2 and the cooling process CD of SMA1.


RESPONSE SPEED

78

Fig. 4-17 Results with PRFC for SMA1 in ambient temperature 24°C

100 150 200 250 300

0

2

4

6

100 150 200 250 3001.3

1.4

1.5

1.6

1.68

100 150 200 250 300

-0.5

0

0.5

1

1.5

2

ResistanceReference

Res

ista

nce

(Ω

)

Time (s)

Volt

age

(V)

Dis

pla

cem

ent

(mm

) (i)

(ii)

(iii)

Vh

Cooing Maintaining

Cooing Maintaining Heating

Vm

C D

C D

E


RESPONSE SPEED

79

Fig. 4-18 Results with PRFC for SMA2 in ambient temperature 24°C

100 150 200 250 300

0

2

4

6

100 150 200 250 3001.3

1.4

1.5

1.6

100 150 200 250 300

0

1

2

ResistanceReference

Res

ista

nce

(Ω

)

Time (s)

Volt

age

(V)

Dis

pla

cem

ent

(mm

)

(i)

(ii)

(iii)

Vh

Maintaining Cooling

Maintaining Cooling Heating

Vm

C E A

C A


RESPONSE SPEED

80

The output displacement is illustrated in Fig. 4-19. It shows that the maximum output

displacement (1.47mm) is the sum of both SMA wires. Part 1 and part 2 are the

available results of cycle for SMA2 and SMA1, respectively. The detailed output

displacement is shown in Fig. 4-20 with two cycles.

Fig. 4-19 Total output displacement with PRFC in ambient temperature 24°C

Fig. 4-20 Detailed output displacement with two cycles for PRFC


100 150 200 250 300

-0.5

0

0.5

1

1.5

2

120 140 160 180 200 220

0.6

0.8

1

1.2

1.4

1.6

Time (s)

Dis

pla

cem

ent

(mm

)

Part 1 Part 2

Time (s)

Dis

pla

cem

ent

(mm

)

Part 1 Part 2

Total

Available


RESPONSE SPEED

81


The arrangement proposed here improves the response speed of the thick SMA wires

significantly in comparison with the binary control. There are , however, a few critical

points needs further consideration.

1. Since the maximum output displacement of both SMA wires is different. To

obtain clear and accurate results, part 1 will be selected to compare with binary

control of SMA2, and part 2 will be compared with binary control of SMA1. As

illustrated in Fig. 4-21, the output displacement with PRFC starts to extend at 10s

during the cooling process. According to the criteria in chapter 3, when the output

displacement is less than 90% of the maximum displacement, the SMA1 starts the

transformation from martensite start phase to martensite finish phase at 13s, and

the latency duration with PRFC TLp=3s. The SMA1 completes the phase

transformation at e=46.5s. Fig. 4-22 shows the results with PRFC for SMA2. The

SMA2 completes the phase transformation at e=43s. More detailed information is

listed in Table 4-3. The average cycle time for the binary control and proposed

method is 54.5s and 39.8s, respectively. The response improvement is given by

%1.275.54

7.14

5.54

8.395.54

(4-8)

Table 4-3 Parameters of the SMA1 and SMA2

Binary control PRFC

Tcd Cycle time TLp Cycle time

SMA1 13s 54s 3s 41.5s

SMA2 14s 55s 2s 38s


RESPONSE SPEED

82

Fig. 4-21 Results with the PRFC and binary control for SMA1


Fig. 4-22 Results with the PRFC and binary control for SMA2


0 10 20 30 40 50 60-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Binary controlProposed

0 10 20 30 40 50 60-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Binary controlProposed

Time (s)

Tcd

TLp

Dis

pla

cem

ent

(mm

)

Time (s)

Dis

pla

cem

ent

(mm

)

Offset

Offset

Cooling

Heating

Cooling Heating

SMA1 SMA2

e f

f

e

Tcd

TLp


RESPONSE SPEED

83

2. Theoretically, the MOSFET should be turned off during the cooling process in

order to obtain rapid cooling response speed. One limitation is that the

microcontroller needs time to read the analog inputs voltage V1, V2 and V3 to

calculate the resistance by turning on the MOSFET and turning off it when the

reading is finished, which makes longer time for the SMA finishes phase

transformation from austenite to martensite. Fig. 4-23 shows the results with or

without reading the input voltage to calculate the resistance with ambient

temperature 24°C. There will be small current through the SMA wire by turning

on MOSFET when reading the analog input voltage, resulting in SMA finishes

the martensite phase at f2=71s instead of f1=68s. It means that the cooling speed

will be slower by calculation the resistance of SMA during cooling process even

if the heating speed is the same. Therefore, when the output displacement with

binary control is detected by displacement sensor, the resistance is calculated as

well by reading the analog inputs in order to compare the output displacement

with proposed method. In addition, as shown in Table 4-2, there is small

difference for the resistance of SMA wires because the calculation of resistance is

affected by the microcontroller, specimen, driver circuit and power source.

3. As shown in Fig. 4-21 and Fig. 4-22, the offset of two cycles during cooling

process is 0.05mm and -0.08mm for SMA1 and SMA2 respectively. The output

displacement (Fig. 4-21) is from SMA1 and SMA2 during the heating and

cooling processes for the proposed method, respectively. Since the maximum

output displacement of SMA2 is 0.71mm, the output displacement with PRFC for

SMA1 declines from 0.81mm and can not reach to zero position during the

cooling process. Then, the offset is positive; since the maximum output


RESPONSE SPEED

84

displacement of SMA1 is 0.81 mm, the output displacement with PRFC for

SMA2 (Fig. 4-22) declines from 0.71mm and the offset is negative. In addition,

the insulation joint which is used to prevent short circuiting needs to be tight

enough to connect SMA wires to prevent offset caused by loosening.

4. As shown in Fig. 4-24, the results of output displacement are very similar with

heating time 5s for 5 tests, however, the offset for maximum output displacement

and martensite finish displacement are 0.02mm and 0.03mm, respectively. It

means there will be small offset for output displacement in each test with the

same heating and cooling time because the output displacement is affected by

hysteresis effect and sensitive to ambient environment. Therefore, the offset for

the output displacement is unavoidable.

Fig. 4-23 Binary control with or without resistance calculation


0 20 40 60-0.5

0

0.5

1

1.5

Time (s)

Dis

pla

cem

ent

(mm

)

With reading

Without reading

f1 f2

Heating

Cooling


RESPONSE SPEED

85

Fig. 4-24 Results with the binary control for 5 tests


5. For the two cycles shown in Fig. 4-20, the maximum output displacement is

based on one single SMA wire even though two SMA wires are used in the

experiment with PRFC. The total output displacement is 1.47mm, however the

effective output displacement is 0.71mm and 0.81mm. Therefore, the results of

rapid response speed is achieved on the cost of maximum output displacement

10 150.75

0.8

0.85

0.9

0.95

60 65

-0.1

-0.05

0

0.05

0 20 40 60

0

0.5

1

1.5

Time (s)

Dis

pla

cem

ent

(mm

)

Offset Offset

Heating


RESPONSE SPEED

86

which is a limitation for the proposed method.

6. The results only show the improvement of cooling speed with shortening the

latency duration Tcd , the latency duration Tab still exists even though is small

compared with Tcd. As shown in Fig. 4-15, there is still small hysteresis duration

Tn when the output displacement is maintained at martensite start displacement

during the cooling process when the power is turned off. Moreover, there is short

latency duration TLp with the PRFC. It means the latency duration caused by

hysteresis effect cannot be eliminated totally. But it does not deny the

effectiveness of the proposed method.

7. Comparing with the research in reference [5], there is no limitation caused by

Peltier device. The advantages are as follows.

(i) There is no need to heat the Peltier in order to heat SMA, resulting in

saving energy.

(ii) Since the two SMA wires are connected by insulation joint, there is no

heat transfer between adjacent segments.

(iii) The SMA wires will not shift to adjacent units, as the SMA wire shrinks

and expands. Therefore, there is no error caused by adjacent segment.

(iv) At last, the experimental apparatus is light and convenient because of

without Peltier models in the apparatus.

4.6 Chapter Summary

An SMA actuator structure using two connected SMA wires which is able to generate

rapid response for thick SMA actuators is proposed. The results with the proposed

PRFC (Phase resistance feedback control) using the concept of phase transformation


RESPONSE SPEED

87

resistances that divided the hysteresis loop into four parts, enable a shortening of

latency duration with two connected SMA wires coordinated to use the phase

resistances as feedback than with the binary control. Experimental results also

demonstrated that the average cycle time was 27.1 percent shorter than with binary

control.

To accurately identify phase resistances, experiments have shown that it is important

to determine the major hysteresis loop. It is also important to avoid overheating the

SMA wires by controlling the heating time which could otherwise slow the response

speed greatly.


RESPONSE SPEED

88


RESISTANCE AND DISPLACEMENT AS FEEDBACK

89

CHAPTER 5:

IMPROVEMENT OF RESPONSE SPEED

USING PHASE RESISTANCE AND

DISPLACEMENT AS FEEDBACK

5.1 Introduction

There are many researches on improvement of the response speed in the past as

mentioned in chapter 3 and chapter 4 [74, 80]. Conventional SMA actuator systems

consist of heating the entire length of SMA wire with electric current and cooling with

natural convection [62, 67], the wire shrinks or extends at the same time. There are long

latency durations for thick SMA wires, the response speed is slow which has been

discussed in chapter 4. In contrast, an approach, which separately controls two

connected SMA wires, making individual SMA wire can shrink or extend at different

time with the same maximum output displacement as an entire SMA wire, is proposed

in this chapter. The motivations will first be explained. In section 5.3 and 5.4, the

method and results will be described. Some discussions and conclusions about the

results are also presented in section 5.5 and 5.6, respectively.


In chapter 4, the PRFC demonstrates more rapid response speed than binary control.

However, the maximum output displacement is only detected from one single SMA wire.



90

Here, an alternative control method, phase resistance and displacement feedback control

(PRDFC), combining both the phase resistance and displacement as feedback, is

proposed to obtain rapid response speed as well. It minimizes cooling time by

shortening the long latency duration of thick SMA wires and the total output

displacement is the same as traditional control method. Experimental results here show

that rapid response speed is achieved using this method in comparison with the case in

which only displacement is used as feedback.

5.3 Method

5.3.1 Phase Resistance with Displacement Feedback Control (PRDFC)

Traditionally, a data collected from a displacement sensor can be used as feedback for

only one SMA wire in a position control. It is difficult to control the output

displacements of two SMA wires at the same time when they shrink or extend randomly

because they will interfere with each other. To prevent the two SMA wires from mutual

interference and obtain accurate position control results, a few technical issues must be

considered:

1. When the SMA wire completes the transformation from martensite to austenite, it

needs to be maintained in martensite starting phase which is ready to extend

without any changes in the output displacement;

2. When one SMA wire completes the transformation from martensite to austenite, the

other needs to start the phase transformation quickly to guarantee continuity of

output displacement, or vice-versa.

The critical aspect of the PRDFC method is to shorten the total cooling time by

http://dict.youdao.com/w/mutual/

http://dict.youdao.com/w/interference/



91

switching the reference input from phase resistances to displacement with two

connected SMA wires that are coordinated, or vice-versa.

To justify the concept of PRDFC, a step signal is used as reference input for a

position control of SMA actuator first. Fig. 5-1 shows the basic theory behind this

method, using the definitions in Fig. 4-2, Fig. 4-3 and Table 4-1, and it can be explained

as follows.

Fig. 5-1 Schematic of step reference for the PRDFC method

As shown in Fig. 5-1(i), the step signal is divided into two parts, part 1 is used as

reference input signal for SMA1, part 2 is used as reference input signal for SMA2.

Since the data collected from the displacement sensor can be used as feedback for only

one SMA wire, the SMA wire need to be maintained at Rms to prevent from any changes

in the output displacement when the other one extends or contracts. As shown in Fig.

5-1(ii), the reference input switches from displacement to resistance for SMA1 at b, and

a

Dis

pla

cem

ent

Time b c d

Res

ista

nce

(i)

(ii)

Part2

Part1 SMA1

SMA2

SMA1

D1

D2

0

Rms



92

during section bc the output displacement is maintained. This means that only one SMA

wire provides the output displacement in each part.

During section ab, part 1 is used as the reference displacement for SMA1, and once

the total output displacement reaches D1 at b, the reference input quickly switches from

displacement to resistance and the resistance of SMA1 is maintained at Rms. The result

is that there is no displacement output from SMA1 during section bc.

Fig. 5-2 Schematic of ramp reference for the PRDFC method

During section bc, part 2 is used as reference displacement input for SMA2 from b,

immediately. The data collected from the displacement sensor can be used as feedback

to control the position of SMA2 because SMA1 is maintained in martensite starting

phase and it is ready to extend without any changes in the output displacement.

During section cd, once the total output displacement reaches D2 at c, both the power

for SMA1 and SMA2 are turned off to achieve quickly cooling speed. Since SMA1 has

a

Dis

pla

cem

ent

Time b c d

Res

ista

nce

(i)

(ii)

Part2

Part1

SMA1

SMA2

SMA1

D1

D2

0

Rms



93

completed the phase transformation from austenite to matensite starting during section

bc, the latency time Tcd of SMA1 is shortened, making it possible to obtain fast cooling

response speed during section cd. In order to obtain the maximum output displacement

of SMA continuously, the reference input needs to increase step by step. Since the

sampling time is 0.05s, the time of each step for reference input needs to be less than

sampling time. In this chapter, the ramp signal is used in the position control to get the

maximum output displacement. Fig. 5-2 shows the basic theory behind this method as

well, using ramp signal as reference input. Part 1 is used to obtain the maximum output

displacement of SMA1. Then, the Rms of SMA1 can be used as feedback to maintain the

output displacement of SMA1.

5.3.2 Control System

Fig. 5-3 Block diagram of PRDFC, (i) Displacement feedback control; (ii) Phase

resistance feedback control

As discussed in the introduction section, many efforts have been made to model and

control behavior of SMA actuators. In this section, a new control system combined by

Displacement Displacement

PWM SMA

Resistance

Rms

e +

-

-

(i)

(ii)



94

displacement and resistance feedback is proposed here to apply the PRDFC method to

control SMA actuator. Fig. 5-3(i) and Fig. 5-3 (ii) show the displacement and resistance

feedback system, respectively. The control system switches from resistance to

displacement feedback control for the position control of SMA1 or SMA2; the control

system switches from displacement to resistance feedback control to maintain the output

displacement of SMA1 or SMA2. The reason that switches control system between

displacement feedback control and resistance feedback control is that there is no

displacement output from SMA wires by maintaining the resistance of SMA wires at Rms

when they complete phase transformation from martensite to austenite, making it

possible to obtain fast response speeds during the cooling processes by shortening the

latency duration without reducing the accuracy of position control.

Fig. 5-4 Schematic of the experimental setup for displacement feedback control

For the displacement control of SMA1 or SMA2, the displacement is measured by

the displacement sensor and resistance is calculated by Eq. (3-1), using the data sent by

microcontroller. To be able to use the phase resistance and displacement as feedback, a

PI controller is installed. The PI controller is denoted by PWM which is sent to

MOSFET and converted to heat voltage. It can be calculated by Eq. (4-6) and Eq. (4-7).

L=LSMA1+LSMA2

Bias spring

Laser

sensor

sensor

Reflector

Load cell



95

The experimental setup is the same as Fig. 4-7 with PRDFC. To be able to compare

PRDFC with traditional displacement feedback control, it is necessary to use the same

length of SMA wire by sending the same PWM value (calculated by PID controller in

Fig. 4-8) to heat the SMA wires. Then, as shown in Fig. 5-4, the length of SMA wire

with traditional displacement feedback control, L, is expressed by

L=LSMA1+LSMA2 (5-1)

where LSMA1 and LSMA2 are the length of SMA1 and SMA2, respectively.

5.4 Results

5.4.1 Tuning PID Parameters

In order to obtain good results with PRDFC, the parameters of resistance feedback in

the PID controller based on Eq. (4-6) are the same as used in chapter 4. For the

parameters of displacement feedback, it needs to be tuned again. Fig. 5-5 shows the

results of PI control using displacement as feedback. When Kp=500 and Ki=0, the

maximum output displacement is small and there are large steady-state error since the

input voltage which is used to heat the SMA wire is small. When Kp=1000 and Ki=0, the

maximum output displacement increases. However, there is still steady-state error.

When Kp=1000 and Ki=0.2, the tracking performance is the best. With Kp=1000 and

Ki=1, the output displacement is the worst since the input voltage changes largely

shown in Fig. 5-6.



96

Fig. 5-5 Results with different parameters of PI controller


Fig. 5-6 Input voltage for different parameters of PI controller


0 20 40 60 80-0.5

0

0.5

1

1.5

kp=500, ki=0kp=1000, ki=0kp=1000, ki=0.2kp=1000, ki=1

0 20 40 60 800

1

2

3

4

5

6

kp=500, ki=0kp=1000, ki=0kp=1000, ki=0.2kp=1000, ki=1

Time (s)

Dis

pla

cem

ent

(mm

)

Time (s)

Volt

age

(V)



97

According to the method shown in Fig. 5-1, experiments are conducted with step

signal as reference input. The maximum output displacement of step is 1.4mm, and then

the maximum output displacements for SMA1 wire are 0.8mm (0.01mm offset from the

maximum output displacement 0.81mm) which leads to a major hysteresis loop of

displacement-to-resistance, making it possible to use the phase resistances as feedback

during the phase resistance feedback control. As shown in Fig. 5-7, the resistance of

SMA1 decreases from 10s since the displacement is used as feedback from 10s to 50s.

From 50s to 90s, the resistance of SMA1 is maintained at Rms . As shown in Fig. 5-8, the

output displacement is unchangeable and maintained at 0.74 mm during the maintaining

period and the SMA1 completes the cooling process at f=135s. Therefore, it is possible

to actuate SMA2 using the displacement as feedback from 50s to 90s because the

SMA2 will not be interfered by the output displacement of SMA1.

Fig. 5-7 Results of resistance for SMA1 with PRDFC in ambient temperature 24°C;

resistance control: Kp=4000, Ki=0.2

0 50 1001.3

1.4

1.5

1.6

1.7

1.8

1.9

2

ResistanceReference

Time (s)

Res

ista

nce

(Ω

)

Maintaining

Cooling



98

Fig. 5-8 Results of output displacement for SMA1 with PRDFC


5.4.2 Results with PRDFC

The experimental results of the proposed PRDFC and conventional displacement

feedback control (based on Eq. (4-6) with Kp=1000 and Ki=0.2 as parameters, e(t) is the

signal error of displacement) are shown in Fig. 5-9. And the traditional method leads to

latency more latency duration (Tcd=5.5s) than proposed method, which is caused by

hysteresis effect of SMA (same phenomenon observed in Fig. 3-9). It is observed that

the proposed PRDFC behaves more rapid response speed than the traditional

displacement feedback control during the cooling process from 90s to 150s, though both

systems in this test have similar tracking trajectory during the heating process from 10s

to 90s. Since during tracking period of SMA2 from 50s to 90s, the latency duration of

SMA1 is shortened, which leads to rapid cooling speed during the cooling process from

90s when the power is turned off. According to criteria to decide the martensite finish

time with horizontal line mentioned in section 3.5, the proposed and traditional method

complete the cooling process at e=138s and f=148s, respectively.

0 50 100 150 200-0.5

0

0.5

1

ResistanceReference

Time (s)

Dis

pla

cem

ent

(mm

) Maintaining

Cooling

f

0.74mm



99

Fig. 5-9 Results of PRDFC and traditional method in ambient temperature 24°C;

displacement control: Kp=1000 and Ki=0.2; resistance control: Kp=4000 and Ki=0.2

Fig. 5-10 Results of resistance for SMA2 with PRDFC in ambient temperature24°C;

displacement control: Kp=1000 and Ki=0.2

0 50 100 150-0.5

0

0.5

1

1.5

ProposedTraditionalReference

0 50 1001.3

1.4

1.5

1.6

1.7

1.8

1.9

2

Time (s)

Dis

pla

cem

ent

(mm

)

e f

Time (s)

Res

ista

nce

(Ω

)

Heating Cooling

Heating

Part 1

Part 2

0.06mm

Tcd

TLp



100

Fig. 5-11 Results of PRDFC and traditional method in ambient temperature 24°C;



resistance control: Kp=4000, Ki=0.2

0 50 100 150-0.5

0

0.5

1

1.5

ProposedTraditionalReference

0 50 1001.35

1.45

1.55

1.65

1.75

1.85

1.952

ResistanceReference

Time (s)

Res

ista

nce

(Ω

)

Maintaining Cooling

Heating

Part 1

Part 2

o

Time (s)

Dis

pla

cem

ent

(mm

)

e f

Heating

-0.07mm

Tcd

TLp



101


displacement control: Kp=1000 and Ki=0.2

Fig. 5-10 shows the results of resistance for SMA2. It also demonstrates the variation

of resistance using displacement as feedback during heating process. When the power is

turned off from 90s, the resistance increases quickly during the cooling process.

In addition, experiments are also conducted with ramp signal using the same PI

controller as step as reference input to demonstrate the feasibility of the proposed

method. Fig.5-11 shows the experimental results of the proposed PRDFC and traditional

control with ramp signal. Part 1 and part 2 are used as displacement feedback for SMA1

and SMA2, respectively. The tracking trajectory of PRDFC is also the same as that of

displacement feedback control plotted using the black line. It is observed that the

proposed PRDFC behaves more rapid response speed than the traditional method during

the cooling process from 45s to 130s as well. Since during tracking period of SMA2

from 30s to 45s, the latency duration of SMA1 is shortened, which leads to rapid

0 50 100 1501.3

1.4

1.5

1.6

1.7

1.8

1.9

2

Time (s)

Res

ista

nce

(Ω

)

Cooling Heating



102

cooling speed during the cooling process from 45s when the power is turned off. And

the traditional method leads to more latency duration (Tcd=6s) than proposed method.

According to criteria to decide the martensite finish time with horizontal line mentioned

in 3.5 as well, the proposed and traditional method complete the cooling process at

e=108s and f=120s, respectively.

Fig. 5-12 and Fig. 5-13 show the results of resistance with PRDFC. In Fig.5-12, the

resistance of SMA1 decreases from 10 s since the displacement is used as feedback

from 10s to 30s. During this heating process, the SMA1 completes the transformation

from martensite to austenite. From 30s to 45s, the resistance of SMA1 is maintained at

Rms, which makes the output displacement unchangeable during the maintaining period

to actuate SMA2 using the displacement as feedback because the SMA2 will not be

interfered by the output displacement of SMA1. During maintaining process, the SMA1

completes the transformation from austenite finish phase to martensite start phase which

leads to a shortening latency duration Tcd.


The proposed method demonstrates more rapid response speed than traditional

displacement feedback control. There are, however, a few critical points needing further

consideration.

1. As shown in Fig. 5-9 and Fig. 5-11, both the step and ramp signals show that the

proposed method lead to more rapid response speed than traditional displacement

feedback control because the proposed method shortens the latency duration Tcd

of SMA1 which is caused by the hysteresis effect. However, as mentioned in



103

section 4.5, there is still latency duration TLp which can not be eliminated totally.

In addition, the parameters of tuning PI controller is important since the best and

similar position tracking can eliminate the possibility that the rapid speed of

proposed method arises from other factors. Another limitation is only the latency

duration of SMA1 is shortened in these tests even though two SMA wires are

used in the experiments.

2. As shown in Fig. 5-9 and Fig. 5-11, the speed of heating process with traditional

method for step input 0.8mm is faster than with the proposed method. Because

the SMA length for the traditional method is 280 mm, however, the SMA length

for the proposed method is 140mm for part 1. With the same PID parameter and

reference input, the maximum output displacement for the traditional method is

larger than proposed method in part 1, resulting faster response speed during

heating process. Since the remaining maximum output displacement of both

methods is the same for the part 2, say 0.71mm, the speed of heating process is

almost the same.

3. Concerning about PRDFC, it is important to make two SMA wires output

displacement continuously. Once there is no output displacement from SMA1,

SMA2 should be actuated quickly. The part o caused by thermal expansion of

SMA2 (Fig. 5-11) leads to less accurate for the position tracking control

compared with tradition method. In addition, it is important to distinguish the

maximum output displacement of SMA wire to avoid overheating with PRDFC.

A maximum ramp signal, 1.6mm(1.0mm for SMA1, 0.6mm for SMA2), is used

as reference input to verify this statement. As shown in Fig. 5-14, part 1 and part

2 are used as displacement feedback for SMA1 and SMA2, respectively. When



104

the maximum reference input for the SMA1 is 1.0mm, but the maximum output

for SMA1 is only m=0.8mm (0.01mm offset from the maximum output

displacement 0.81mm), then SMA1 will be over heated from m to n, which leads

to more overshoot and undershoot than traditional method from 30s to 40s.

4. As shown in Fig. 5-9 and Fig. 5-11, the maximum offset for the output

displacement is respective 0.06mm and -0.07mm when SMA finishes the

transformation from austenite to martensite during the cooling process at f and e,

which is arisen from the same reason mentioned in section 4.5.

Fig. 5-14 Results of overheating for SMA1 in ambient temperature 24°C;


0 50 100 150-0.5

0

0.5

1

1.5

2

Proposed TraditionalReference

30 40 50 60

0.8

1

1.2

n m

Time (s)

Dis

pla

cem

ent

(mm

)

Part 1

Part 2



105

5.6 Chapter Summary

An SMA actuator structure and control system using two connected SMA wires

which is able to generate rapid response for thick SMA actuators is proposed. Two sets

of signal are used as reference input to test the results of both proposed and traditional

method. The results show that using only displacement as feedback leads to slower

cooling speeds than with the proposed PRDFC.

Since experiments demonstrated that the thick SMA wires suffer from significant

hysteresis effects with long latency duration (chapter 3), to obtain a rapid response of

the SMA actuators, this chapter proposes a PRDFC (Phase resistance with displacement

feedback control) method using the concept of phase transformation resistances that

dividing the hysteresis loop into four parts (chapter 4).

In the experiments, SMA1 is used in the position tracking control with displacement

as feedback first. Then SMA2 is used in the position tracking control when SMA1 is

maintained using resistance as feedback. This enables a shortening of the latency

duration with two connected SMA wires coordinated by using the phase resistance and

displacement as feedback when compared with the case where only displacement

feedback is used.



106

.


ROGERS MODEL

107

CHAPTER 6:

MODELING OF AN SMA ACTUATOR BASED

ON THE LIANG AND ROGERS MODEL

6.1 Introduction

In modeling the hysteresis of an SMA to accurately estimate the behavior of the SMA

actuator, many models have been proposed during the last decade. However, the main

difficulty in modeling SMA actuators is due to the non-linear saturated hysteresis effect

during the phase transformation from martensite to austenite, or vice-versa. Hirose,

Ikuta and Umetani proposed a two-phase model for SMA using the sub-layer model, a

commonly used method to describe nonlinear stress-strain relationships in solid

mechanics [86]. Tanaka developed a thermo-mechanical law that governs the

stress-strain behavior of SMA elements [30]. Williams and Mohammad introduced a

model of an SMA actuator which consists of four sub-models: a heat transfer model, an

SMA thermo-mechanical model, a phase transformation kinetics model, and a

dynamic/kinematic model [87]. However, these models did not show the minor

hysteresis relationship between input and output even though they can precisely

reproduce the thermo-mechanical behavior of SMA. Dutta and Ghorbel proposed a

model using a differential hysteresis model capable of representing the major and minor

hysteresis loops [38]. However, this model can not show the relationship between

martensite start temperature and the maximum temperature during heating process of

each minor hysteresis loop. In this chapter, the motivations will first be explained. In


ROGERS MODEL

108

section 6.3 and 6.4, the method and results will be described. Some discussions and

conclusions will be shown in section 6.5 and 6.6.


In this chapter, a successful empirical relation proposed by Liang and Rogers is

introduced in order to model the major hysteresis behaviors of SMA actuators, which

represents the amount of austenite fraction transformed on a temperature [34]. Liang

and Rogers described a unified, thermomechanical constitutive model to quantitatively

predict the stress-strain relation and shape memory behavior. It also focused on shape

memory effects and provided a theoretical guide to the design of SMA based on

intelligent material and structures. However, it is difficult to apply the method to

practical application without representing the minor hysteresis loops, successfully.

Based on the empirical relation of the Liang and Rogers model, a modified Liang and

Rogers model is demonstrated to consider the major and minor hysteresis behaviors. An

experimental setup used for verification of the modeling system is presented and some

test series are conducted to identify the parameters of the modified Liang and Rogers

model. The reasonable agreement achieved between curves predicted by the modified

Liang and Rogers model and the measured data shows that the proposed model is

efficient in modeling the hysteresis of the SMA actuator system.

6.3 Method

6.3.1 Thermal Model of Heat Transfer and Temperature

As mentioned in chapter 2, an SMA returns to some predefined shape or size when


ROGERS MODEL

109

subjected to an appropriate thermal procedure, and is known as a shape memory effect.

The shape memory effect arises from temperature and stress dependent shifts in the

crystalline structure of the SMA, shifts between martensite and austenite phases. The

system gains heat energy from an electrical current, and loses part of it to the

environment. As suggested in Fig. 6-1, this model considers an SMA element as a

three-element system in which thermal energy is concerted into a phase transformation

and then into mechanical work. In this section, a new mathematical model of the SMA

actuator is introduced, including the major and minor hysteresis loops to model the

transformation model of SMA actuator.

Fig. 6-1 Block diagram model of SMA

In this section, the heat transfer problem of the SMA wire is described. The balance

of the heat energy governs the temperature of the SMA actuator. For a spring-biased

SMA wire, the thermal model between input voltage V and the output temperature T ,

which is shown in module 1 (Fig. 6-1), is a first-order system given by

)()(

400

20

2

0

ambTThLdR

tV

dt

dTLdc

(6-1)

Module 1 Module 2

Module 3


ROGERS MODEL

110

where is the density of the SMA; c is the specific heat coefficient; 0L is the length

of the SMA wire; 0d is cross-sectional diameter of the SMA; V is the voltage applied; R

is the resistance; h is the convection heat transfer coefficient, and ambT is the ambient

temperature.

Fig. 6-2 Schematic of the input voltage

Since the actual temperature of the SMA wire is not measured in the experiments,

direct validation of the heat transfer model mentioned above is not possible. However,

the simulation result is able to demonstrate the thermal transfer model. Fig. 6-2 shows

that six triangular voltages are set as the input voltage for simulation. The maximum of

input voltage is 2V for the major loop and the others are for the minor loops. Fig. 6-3

shows the simulation results of the output temperature obtained from Eq. (6-1)

corresponding to the input voltage shown in Fig. 6-2.

0 200 400 600 8000

0.5

1

1.5

2

Volt

age

(V)

Time (s)


ROGERS MODEL

111

6.3.2 Phase Transformation and Mechanical Model

During the heating process, a phase transformation occurs from martensite to

austenite, while during the cooling process, the opposite transformation occurs, and

SMA wires show a hysteresis effect during both phase transformations. The extent of

austenite to martensite tansformation is characterized by the martensite fraction m .

Martensite fraction is defined as the volume fraction of M phase present in the SMA at

any instant. Therefore, 10 m . As shown in Fig. 6-4, the transformation is

characterized by the initial and finish temperatures. MST and MFT are the initial and

final temperatures of martensite, while AST and AFT are the initial and final

temperatures of austenite, respectively.

Fig. 6-3 Schematic of the output temperature

0 200 400 600 80020

30

40

50

60

70

80

90

Time (s)

Tem

per

ature

(

)


ROGERS MODEL

112

Fig. 6-4 Schematic of martensite fraction-temperature hysteresis

The classical Liang and Rogers model uses trigonometric functions to characterize

the hysteresis effect of module 2 for the SMA actuators. During the heating and cooling

processes, the functions of the martensite fraction mh and mc are expressed by

2

21

1

0

)(cos15.0

1

MT

MTM

MT

TT

CA

FTT

ASAF

A

AS

mh

(Heating) (6-2)

Heating

Cooling

Temperature

Mar

tensi

te f

ract

ion

0

1

TMF TAS TMS TAF


ROGERS MODEL

113

4

43

3

0

)(cos15.0

1

MT

MTM

MT

TT

CA

FTT

MFMS

M

MF

mc

(Cooling) (6-3)

where M1= TAS +F/(A∙CA); M2= TAF +F/(A∙CA), M3= TMF+F/(A∙CM); M4= TMS +F/(A∙CM);

T is the temperature of the SMA wire; F is the pre-tension; A is the cross section area of

the wire; CM is the stress rate of martensite, and CA is the stress rate of austenite.

Then the austenite fractions during the heating and cooling processes can be defined

as mhah 1 and mcac 1 , respectively. Since the effect of pre-tension is small

in the experiments, the equations proposed by Liang and Rogers that model such

transformations as function of temperature are simplified as

AS

AFAS

AF

ASAF

ASah

TT

TTT

TT

TT

TT

0

)(cos15.0

1

(Heating) (6-4)

MF

MSMF

MS

MFMS

MFac

TT

TTT

TT

TT

TT

0

)(cos15.0

1

(Cooling) (6-5)

where ah and ac are the amount of austenite fractions during the heating and cooling

processes, respectively.

However, the Liang and Rogers model only represents the major hysteresis loop of


ROGERS MODEL

114

phase transformation without considering the martensite starting temperature of minor

loops. A typical austenite fraction-temperature hysteresis schematic is shown in Fig. 6-5

[38]. The hysteresis loop corresponding to complete phase transformation is called the

major hysteresis loop, while incomplete phase transformation yields minor hysteresis

loops within the major hysteresis loop. The martensite starting temperature of each

minor loop is the same value as the major loop [38].

According to the experimental data described in section 6.4, the minor hysteresis

loops can be revised in a new shape shown in Fig. 6-6. The martensite starting

temperature of each minor loop is different. The solid line represents the major

hysteresis loop and the dashed lines are for the minor loops. Since the transformation

temperature variation caused by the applied stress is small in this experiment, we

assume that the phase transformation temperatures are constant throughout for major

and minor hysteresis loops.

If ASi TT , then )(Tahi =0, and therefore, only the case of ASi TT is considered.

For a hysteresis loop, the austenite fraction ahi during the heating process is

expressed by

ASi

AFiAS

AFi

ASAF

ASahi

TTT

TTTT

TTT

TT

TTT

0

)(cos15.0

1

)( ),,2,1( Ni (6-6)

where Ni ,,3,2,1 ; iT is the maximum temperature during the heating process of a

hysteresis loop, including minor hysteresis loops. However, Eq. (6-6) is derived from

Eq. (6-4) without modified minor hysteresis loops of heating process.


ROGERS MODEL

115

Fig. 6-5 Schematic of typical austenite fraction-temperature hysteresis

Fig. 6-6 Schematic of austenite fraction-temperature hysteresis with modification

Temperature

Fra

ctio

n

0

1

TMF TMS TAS TAF

Heating

Cooling

Aust

enit

e fr

acti

on

Temperature

0

1


ROGERS MODEL

116

When minorfminors TTT i , then the austenite fraction increases first, and is

maintained unchanged, then decreases during the cooling process; the equation of the

increase and maintaining stages acii is expressed by

iiMSiiiahi

iiiiiahi

acii TTTTzT

TTTTzTT

ii)()(

)()()(

(6-7)

where iiT is the starting temperature of the maintaining stage and can be expressed by

iiiiiiiiii TTTNTT minminmax )( , iiiiii TTT maxmin (6-8)

where iiTmax and iiTmin are the maximum and minimum of iiT . iiNT can be expressed

by

iiNT0

1

1

2

2

3

3

4

4

5

5 aNTaNTaNTaNTaNTa iiiii (6-9)

where iNT can be expressed by

minorsminorf

minors

TT

TTNT i

i

, fi TTT minorminors (6-10)

where minorsT and minorfT is the starting and finishing temperature with increase stages

of cooling process, respectively. MSiT is the martensite starting temperature of a minor

hysteresis loop; )(Tz i is defined as the function for the cooling process in the minor

hysteresis loop.

In order to make sure 1)(0 Tacii and simplify the equation of )(Tz i , the

temperature is normalized. )(Tz i can be expressed by

increase

maintaining maintaining

maintaining


ROGERS MODEL

117

iiMSiii

iii

iii

ii

i

TTTjTz

TTTTT

TTj

Tz

ii)(

)(

)( (6-11)

where ij is the constant for a minor hysteresis loop.

The martensite starting temperature MSiT , which must be determined to model minor

hysteresis loop, is expressed by

minorsminorsminorf )( TTTNTT MSiMSi , minorfminors TTT i (6-12)

where the normalized resistance MSiNT is expressed by

MSiNT0

1

1

2

2

3

3

4

4 mNTmNTmNTmNTm iiii (6-13)

where 4m , 3m ,

2m ,1m and 0m are the parameters obtained by polyfit of Matlab.

When minors1 TTT i and Ni TTT minorf , then 0)( Tz i , there are only

maintaining stages. Therefore, the martensite starting temperature MSiT can be

expressed by

eTqTiMSi ahi )( (6-14)

where q and e are the constants.

During the cooling process, the austenite fraction for a loop can be expressed by

MF

MSiMF

MSii

MSiacii

MFMSi

MF

acii

aci

TT

TTT

TTT

TTT

TT

T

T

)(

0

)(cos15.0

)(

)(

(6-15)

For the mechanical model, the module 3 (Fig. 6-1) shows the output displacement D,

which combines the thermal model and phase transformation model developed above, is


ROGERS MODEL

118

expressed by

coolingg

heatinggD

aci

ahi

(6-16)

where g is constant parameter.

With the three models mentioned above, the hysteresis loops of input voltage and

output displacement including the major and minor loops can be plotted. The

parameters of each loop can be obtained according to the experimental results which

will be presented in the following.

6.4 Results

The experimental setup of the proposed SMA actuator was the same as Fig. 3-5 in

chapter 3. The parameters of the experiments are listed in Table 6-1. To accurately

identify the parameters of the modified Liang and Rogers model formulated for

modeling the saturated hysteresis nonlinearity of an SMA actuator, the input voltage

applied to the SMA actuator in the training process is a slow decaying ramp signal,

making it possible to allow the temperature to stabilize, as in the steady state the

temperature will be decided by the applied voltage [62]. As shown in Fig. 6-7, the

slopes of the decay reversal curves are set to ±5.88×10-3

in the training process of the

modified Liang and Rogers model, including the maximum and minimum at 2.35V and

1.47V, respectively. Fig. 6-8 shows the results of the experiments with input

voltage-output displacement hysteresis loops for the SMA actuator using the input

voltage in Fig. 6-7. When the input voltage is below 1.47V or above 1.88V, the minor

hysteresis loops can be expressed by the modified Liang and Rogers model without the


ROGERS MODEL

119

increase stage. However, minor loops with input voltage inputV , 1.47V < inputV <1.88V,

where small changes in the input voltage lead to considerable displacement changes,

need to be expressed by the modified Liang and Rogers model with the increase stage.

Fig. 6-7 Schematic of the input voltage

Table 6-1 Parameters of the experiments

Ambient temperature 22°C SMA diameter 0.5mm

MOSFET K2232 SMA length 140mm

Power supply 5V Spring stiffness 653.3N/m

Microcontroller Arduino Pretension force 2.75N

0 200 400 600 800 10000

0.5

1

1.5

2

2.5

Volt

age

(V)

Time (s)


ROGERS MODEL

120

Then, parameter identification for the proposed model, simulation results by the

proposed model, and a comparison with the experimental data are presented. Estimates

for parameters used in Eq. (6-13) and Eq. (6-14) are obtained by curve fitting. The

remaining parameters are identified using the actual displacement measured by the laser

sensor, as actual temperature measurements are not available.

Based on Eq. (6-6) and Eq. (6-15), Fig. 6-9 shows the results of simulated austenite

fraction versus time, including the major and minor hysteresis loops of the SMA

actuator. The six modified Liang and Rogers model parameters are listed in Table 6-2.

minorsT , 2T , 3T , 4T , and minorfT are selected to identify the parameters in Eq. (6-10),

(6-12), (6-13), while minorsT , minorfT , and AFT are for the parameters in Eq. (6-14). The

corresponding major and minor loops of austenite fraction versus temperature are

shown in Fig. 6-10. It is evident that the hysteresis loops in Fig. 6-6 would qualitatively

match the hysteresis loops in Fig. 6-10. To obtain the martensite starting temperature

MSiT , Fig. 6-11 and Fig. 6-12 show the simulation results of MSiT based on the Eq.

(6-13) and Eq. (6-14), respectively. The results show that the martensite starting

temperature MSiT can be predicted.

With the relationship between input voltage and output temperature in Eq. (6-1) of

module 1, the input temperature and output austenite fraction in Eq. (6-6) and (6-15) of

module 2, the input austenite fraction and output displacement in Eq. (6-16) of module

3, as shown in Fig. 6-13, the input voltage VS output displacement with the modified

Liang and Rogers model is plotted, including the major loop plotted in a solid line and

the minor loops plotted in dashed lines.


ROGERS MODEL

121

Fig. 6-8 Schematic of the displacement VS input voltage

Fig. 6-9 Simulated austenite fraction versus time

0 0.5 1 1.5 2 2.5-0.2

0

0.2

0.4

0.6

0.8

1

0 200 400 600 8000

0.2

0.4

0.6

0.8

1Minor loopsMajor loop

Aust

enit

e fr

acti

on

Time (s)

Dis

pla

cem

ent

(mm

)

Voltage (V)


ROGERS MODEL

122

Fig. 6-10 Simulated austenite fraction versus temperature

Fig. 6-11 Curve for fitting the normalized martensite starting temperature

20 40 60 80 1000

0.2

0.4

0.6

0.8

1

Minor loops

Major loop

0 0.2 0.4 0.6 0.8 1-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Fitting curveNormalized temperature

Aust

enit

e fr

acti

on

Temperature (°C)

T1=Tminors

T2

T3

T4

T5=Tminorf

T6=TAF

No

rmal

ized

tem

per

ature

TM

Si (

)

Normalized temperature Ti (°C)

T1=Tminors

T2

T3

T4 T5=Tminorf


ROGERS MODEL

123

Fig. 6-12 Curve for fitting the martensite starting temperature

Fig. 6-13 Simulation results of the output displacement VS the input voltage

0.2 0.4 0.6 0.8 125

30

35

40

45

50

55

Fitting curveMartensite startTemperature

0 0.5 1 1.5 2-0.2

0

0.2

0.4

0.6

0.8

1

Major loop Minor loops

Tem

per

ature

TM

Si (°

C)

Austenite fraction )(i

Tahi

Tminors

Tminorf TAF

Dis

pla

cem

ent

(mm

)

Voltage (V)


ROGERS MODEL

124

Table 6-2 Simulation parameters

Parameter Value Parameter Value

6500kgm3 R 1Ω

h 165W/m2°C c 836.8 J/kg°C

q -32.69 e 60.47

AST 50.2°C AFT 80.1°C

MST 28°C MFT 22°C

MSfT 28.9°C MSsT 51.1°C

jf 0 js 0

ahf 0.96 ahs 0.29

Tf 75.9°C Ts 60.8°C

2MST 40.8°C 3MST 32.1°C

2j 0.16 3j 0.19

2ah 0.38 3ah 0.66

2T 63.1°C 3T 68.5°C

22T 61.2°C 33T 59.1

4MST 30.1°C 4T 71.5°C

4j 0.1 44T 65.2°C

4ah 0.82 g 0.96

4m 5.24 3m -12.80

2m 11.50 1m -4.94

0m 1.00


ROGERS MODEL

125


As shown in Fig. 6-14, the output with the modified Liang and Rogers model is

plotted together with the experimental data (colors other than red), with the major loop

plotted in a red solid line and the minor loops plotted in red dashed lines. This figure

clearly shows that the modified Liang and Rogers model can effectively characterize the

hysteresis behavior of the SMA actuator. However, there are some factors needed to be

discussed.

Fig. 6-14 Plot with experimental and simulated data

by the modified Liang and Rogers model

1. The Liang and Rogers model has found widespread use in SMA modeling and

position control, but the limitation has been mentioned above which the

temperature of SMA wire needs to be measured to decide the martensite and

0 0.5 1 1.5 2 2.5-0.2

0

0.2

0.4

0.6

0.8

1

MajorloopMinorloops

Others:Experimentaldata

Dis

pla

cem

ent

(mm

)

Voltage (V)


ROGERS MODEL

126

austenite phase. As shown in Fig. 6-13, the proposed model does not suffer from

this limitation since the simulation results show the relationship between input

voltage and output displacement. Concerning about the simulation and

experimental results, as shown in Fig. 6-14, six models are built to model the

basic shape of the hysteresis loops including major and minor loops. However,

the parameters (Table 6-2) of the model need to be changed once the ambient

conditions changed. For example, the variation of bias force leads to a shift of the

hysteresis. An increase in force causes a shift to the right, a decrease shifts the

hysteresis to the left [81], which leads to modify the parameters to fit the

experimental data. Therefore, it is difficult to use this model in unstable

environment.

2. As shown in Fig. 6-14, the discrepancy between the simulated and experimental

data can be explained as follows. The measured displacement shown in Fig. 6-8

corresponds to the voltage profile in Fig. 6-7. Thus, the output displacement

should be smooth. However, due to the ambient conditions of the experimental

setup are not constant over time and space, the error is unavoidable.

3. As shown in Fig. 6-8, the results of output displacement-voltage can repeat during

the heating process including the major and minor loops. However results during

the cooling process are different with since the martensite start temperature of

each loop is different. It is evident that the SMA actuator behavior is highly

nonlinear due to the complex physics.


ROGERS MODEL

127

6.6 Chapter Summary

In this chapter, a complete mathematical model for a spring-biased SMA actuator is

proposed, including both the major and minor hysteresis loops. With the difference from

reference [38] (Fig. 6-5), the proposed model is capable of simulating the temperature

(especially about the martensite start temperature of each loop), austenite fraction and

the output displacement of the actuator.

Based on the Liang and Rogers model, the modified Liang and Rogers model

including the major and minor hysteresis loops is developed and the model parameters

are adjusted by means of experimental identification procedure. The simulation results

show that good accuracy of the model can be assured by using the modified Liang and

Rogers model, including the increase and maintaining stages (expressed by Eq. (6-7)).

The proposed model can predict the martensite starting temperature of the minor

hysteresis loops, successfully.

Footnote: Junfeng Li, Hiroyuki Harada, Modeling of an SMA actuator based on the

Liang and Rogers model, International Journal of Applied Electromagnetics Mechanics,

Copyright (2013), accepted, with permission from IOS Press.


ROGERS MODEL

128

CHAPTER 7: CONCLUSIONS AND FUTURE WORKS

129

CHAPTER 7:

CONCLUSIONS AND FUTURE WORKS

7.1 Conclusions

In many applications where space, weight and noise can be an issue, SMA actuators

present a potential solution with their high force-to-weight ratio, mechanical

compactness, ease of miniaturisation, as well as their clean and silent operation. With

improved speed, accuracy and controllability, the possibilities of using SMA actuators

in, to name a few, robotics, consumer appliances and bio-medical applications, are

greater now. In this thesis, the research focuses on achieving rapid control of SMA

actuators and the obtained results are documented and discussed. The main content of

this thesis can be summarized in the following.

In chapter 1, the objective, approach and the outline of thesis are introduced.

In chapter 2, literature overview which discusses the past research is presented in this

work, including modeling and control system design. Some research is verified by the

experimental results successfully. In addition, many methods developed using cooling

device, thin SMA wires and new actuator structures to achieve fast response speed are

introduced.

In chapter 3, the latency duration of the SMA wire is investigated. Experimental

results show that the latency duration affected by the ambient temperature, which is due

to the hysteresis effect can be observed.

In chapter 4, according to the definition of phase temperatures, the concept of phase

resistance is defined for the first time. Phase resistances used to divide the hysteresis


130

loop into four parts are applied to shorten the long latency duration of thick SMA wire.

The proposed method, phase resistance feedback control (PRFC), is presented here. The

critical aspect of the PRFC method is to shorten the total cooling time by controlling the

phase resistances. Two SMA wires connected by an insulation joint to prevent short

circuiting will cooperate with each other to verify the possibility of the proposed

methods. In order to show the advantages of the proposed method, the experimental

results are compared with the results of binary control. Since the latency duration of

heating process is shorter than cooling process, only the cooling process is considered in

the proposed method.

In chapter 5, phase resistance with displacement feedback control (PRDFC) is also

discussed, which shows another way to achieve rapid response speed and results are

compared with traditional displacement feedback control as well to demonstrate the

advantages of PRDFC. The central element of PRDFC is to divide the reference input

into two parts which are assigned to both SMA wires, separately. Since there is only one

displacement sensor to detect the position of SMA actuator, it is important to make sure

only one SMA wire shrinks or extends for each reference input part. In order to explain

the concept more clearly, a step signal is used as reference input. Combining the heating

and cooling processes of the two SMA wires, the latency durations of SMA wire is

shortened with the proposed method. And the results with PRDFC using ramp signal

also demonstrate that the proposed method achieves more rapid response speed than

traditional displacement feedback control.

In chapter 6, the complete mathematical model for a spring-biased SMA actuator is

proposed, including both the major and minor hysteresis loops. Based on the Liang and

Rogers model, the modified Liang and Rogers model including the major and minor


131

hysteresis loops is developed and the model parameters are adjusted by means of

experimental identification procedure.

To sum up, the research presented in this thesis represents a significant step forward

for practical SMA actuator applications in the future. Substantial improvements in terms

of speed of SMA actuator control have been made compared with the past work. All of

these have been accomplished with free convection cooling and not in a

temperature-controlled condition in speed and position control system.

7.2 Future Works

The present research is a step forward towards the aim of achieving rapid response

speed control of SMA actuator, and remains some limitations and insufficiency. In the

rapid response speed control system, the latency duration of SMA wire is short if the

diameter is small which makes it difficult to use phase resistance as feedback to obtain

rapid response speed by shortening the latency duration. For the concept of PRDFC

method, good results are demonstrated by the experimental tests. It is possible to test

this method using other different reference input, such as square wave.

Fig. 7-1 Block diagram for the compensation based on the inverse model


132

Due to the hysteresis effect of SMA, it is difficult to control the SMA actuator. To

completely compensate the hysteresis effect of an SMA system, it is important to

develop the exact inverse of the hysteresis model. Generally, as suggested in Fig. 7-1,

for the hysteresis model H and inverse model 1H , the following equation can be

developed if the inverse model exists [62].

uuHHvHy ))(()( 1 (7-1)

here y is the output displacement of modified Liang and Roger model; v is the output

voltage of the modified Liang and Roger inverse model which is used as the

feedforward in the proposed control system; u is the input displacement.

ACKNOWLEDGEMENTS

133

ACKNOWLEDGEMENTS

There are many people who had made contributions, both directly and indirectly,

towards the completion of this thesis. I would like to name a few. First and foremost, I

would like to express my sincerest gratitude to my supervisor, Dr. Hiroyuki Harada.

Harada sensei's help has been extremely enormous, and his enthusiasm has sparked my

own in this wonderful work. This work would never have been completed without his

advice and guidance.

I would also like to thank Prof. Kajiwara, Prof. Kobayashi and Prof. Nakamura who

give me many excellent advices for my research.

I would also like to express my gratitude to Dr. Werawan Manakul, the coordinator of

English Engineering Education Program, who supports my life and research in Sapporo.

I would also like to express my gratitude to my parents, who provided me with

unconditional advice, support and love. They have never been far from my heart.

134

APPENDIX A

135

APPENDIX A

a. Binary Control Code with Matlab

hold on

display('begin');

m=zeros(1,15);

n=0;

PP2=0;

PP3=0;

s = serial('COM5', 'BaudRate', 115200);

fopen(s);

pause(1);

% send data to arduino

fwrite(s,strcat(int2str(0),',',int2str(0),',',int2str(0)),'sync');

for i=1:2500

n=i

temp=fscanf(s); % get data from arduino

tempnum=str2num(temp);

m(i,1:length(tempnum))=tempnum;

% Displacement calculation

dis=5*m(:,5)/1023;

% Force calculation

f=5*m(:,15)/1023;

% Time calculation

APPENDIX A

136

t=m(i,4)/1000;

if t<5;

PP2(i)=0;

PP3(i)=0;

fwrite(s,strcat(int2str(0),',',int2str(PP2(i)),',',int2str(PP3(i))),'sync');

elseif t>5&t2<8

PP3(i)=0;

PP2(i)= 255;


else

PP2(i)=0;

PP3(i)=0;


end

end

display('done');

fclose(s);

delete(s);

APPENDIX A

137

b. PID Controller Code with Resistance as Feedback

kp=4000;

ki=0.2;

kd=0;

input2(i)= sF2(i);

setpoint2(i)=1.47; %resistance feedback

tlast1=0;

tchange=(now-tlast1);

error1(i)=setpoint1(i)-input1(i);

output1(i)=

output1+kp*(error1(i)-e1)+ki*error1(i)*tchange+kd*(error1(i)-2*e1+e2)/tchange;

if output2(i)>0

PP2(i)= 0;

elseif output2(i)<-255

PP2(i)=-255;

else

PP2(i)=-round(output2(i));

end

PP2(i)=- PP2(i); % PP2, 0-255, send to arduino to heat the SMA wire

tlast1=now;

e2=e1;

e1=error1(i);

output1= output1(i);

fwrite(s,strcat(int2str(0),',',int2str(PP2(i)),',',int2str(0)),'sync');

APPENDIX A

138

c. Microcontroller Code

Three PWM outputs and fifteen inputs are designed in this code which can be used to

test three segments of SMA wires. In the experiment, only two outputs are used.

String comdata = "";

int numdata[3] = 0, PWMPin[3] = 3, 4, 5, mark = 0;

int val;

int val1;

unsigned long time;

unsigned int x[3]= 0;

unsigned int y[3]= 0;

unsigned int z[3]= 0;

int analogin[9]= A0,A1,A2,A3,A4,A5,A6,A7,A8;

void setup()

Serial.begin(115200);

for(int i = 0; i < 3; i++) pinMode(PWMPin[i], OUTPUT);

void loop()

int j = 0;

while (Serial.available() > 0) // check to see if there is

data in the bus

APPENDIX A

139

comdata+=char(Serial.read());

delay(2);

val=analogRead(A11);

val1=analogRead(A15);

mark=1;

if(mark==1)

if(comdata.length() > 0)

for(int i = 0; i < comdata.length() ; i++)

if(comdata[i] == ',')

j++;

else

numdata[j] = numdata[j] * 10 + (comdata[i] - '0');

for(int i = 0; i < 3; i++)

digitalWrite(PWMPin[i],HIGH);

APPENDIX A

140

for(int j=0;j<3;j++)

x[i]+=analogRead(analogin[i]);

y[i]+=analogRead(analogin[i+3]);

z[i]+=analogRead(analogin[i+6]);

digitalWrite(PWMPin[i],LOW);

x[i]=(x[i]/3);

y[i]=(y[i]/3);

z[i]=(z[i]/3);

analogWrite(PWMPin[i],numdata[i]);

numdata[i] = 0;

Serial.print(x[0]);

Serial.print(",");

Serial.print(y[0]);

Serial.print(",");

Serial.print(z[0]);

Serial.print(",");

Serial.print(millis());

Serial.print(",");

Serial.print(val1);

Serial.print(",");

Serial.print(x[1]);

APPENDIX A

141

Serial.print(",");

Serial.print(y[1]);

Serial.print(",");

Serial.print(z[1]);

Serial.print(",");

Serial.print(x[2]);

Serial.print(",");

Serial.print(y[2]);

Serial.print(",");

Serial.print(z[2]);

Serial.print(",");

Serial.print(comdata);

Serial.print(",");

Serial.println(val);

mark = 0;

comdata = String("");

delay(10);

142

APPENDIX B

143

APPENDIX B

a. Microcontroller

In the control system, a microcontroller (Arduino Mega 2562, shown in Fig. B-1) is

used to collect the data from displacement sensor. The Arduino Mega 2560 is a

microcontroller board based on the ATmega2560 (datasheet). It has 54 digital

input/output pins (of which 15 can be used as PWM outputs), 16 analog inputs, 4

UARTs (hardware serial ports), a 16 MHz crystal oscillator, a USB connection, a power

jack, an ICSP header, and a reset button. It contains everything needed to support the

microcontroller; simply connect it to a computer with a USB cable or power it with a

AC-to-DC adapter or battery to get started. The Mega is compatible with most shields

designed for the Arduino Duemilanove or Diecimila. Detailed information is listed in

Table B-1.

Fig. B-1 Microcontroller used in experiment

http://www.atmel.com/dyn/resources/prod_documents/doc2549.PDF

APPENDIX B

144

Table B-1 Detailed information for microcontroller

Microcontroller ATmega2560

Operating Voltage 5V

Input Voltage 7-12V

Input Voltage (limits) 6-20V

Digital I/O Pins 54 (of which 15 provide PWM output)

Analog Input Pins 16

DC Current per I/O Pin 40 mA

DC Current for 3.3V Pin 50 mA

Flash Memory 256 KB of which 8 KB used by boot loader

SRAM 8 KB

EEPROM 4 KB

Clock Speed 16 MHz

b. Power Source, Displacement and Force Sensor

Since the SMA wire is heated by current, power source is supplied by TEXIO

Kenwood PA18-5B shown in Fig. B-2. The PA-B series is a high-performance DC

constant-voltage, constant-current power supply unit with 3.5 digit voltage indicator

LEDs and 3-digit current indicator LEDs. The series regulator control allows the user to

vary the output from 0 to the rated output. The output controller, a 10-turn winding type

variable resistor, offers fine control of output voltage and current. It is possible to set the

output voltage and current even the output is off. The output voltage and current may be

checked simultaneously. The PA-B series feature output On/Off control, output sensing,

APPENDIX B

145

and various remote control functions and fully meet various user needs. They have a

wide variety of applications including research and development, prototyping, test,

aging, and systems integration. The following is the features of TEXIO Kenwood

PA18-5B.

Fig. B-2 Power source used in experiment

Features for TEXIO Kenwood PA18-5B:

a. Low ripple, low noise

b. Digital display of voltage & current

c. Series/parallel operation

d. Floating output/voltage remote sensing terminal

e. External analog control for fine adjustments

f. EIA rack size

APPENDIX B

146

In order to detect the output displacement and force of SMA actuator, the

displacement and force are obtained by a KEYENCE LC-2000 laser displacement meter

(Fig. B-3)and a TEDEA-HUNTLEIGH load cell (Fig. 4), respectively. Since the output

displacement of SMA wire is less than 3 mm, the microcontroller can detect the output

voltage from displacement sensor directly when setting the displacement output voltage

from 0 to 3 V. However, the output voltage of load cell can be regulated shown in Fig.

B-4.

Fig. B-3 Displacement sensor used in experiment

Features for KEYENCE LC-2000:

a. Reference distance :40mm

b. Measurement range :±3mm

c. Analog output voltage :±3V

d. Resolution:0.5μm

e. Accuracy: ±10μm ±3%

APPENDIX B

147

Fig. B-4 Force sensor used in experiment

Features for TEDEA-HUNTLEIGH:

a. Capacity range: 5kg

b. Only 22mm high

c. Aluminum construction

d. Single point 350 x 350mm

e. IP66 protection

f. OIML R60 and NTEP approved

148

REFERENCES

149

REFERENCES

[1] Z. Wang, G. Hang, J. Li, Y. Wang and Kai Xiao, A micro-robot fish with embedded

SMA wire actuated flexible biomimetic fin, Sensors and Actuators A: Physical, Vol.

14, No. 2(2008), pp. 354–360.

[2] K. Ikuta, M. Tsukumoto and S. Hirose, Shape memory alloy servo actuator system

with electric resistance feedback and application for active endoscope, IEEE

International Conference on Robotics and Automation,Vol. 1, (1988), pp. 427-430.

[3] R. Featherstone and Y. H. Teh, Improving the speed of shape memory alloy

actuators by faster electrical heating, Experimental Robotics IX, Vol. 21, (2006), pp.

67-76.

[4] S. Vollach and D. Shilo, The mechanical response of shape memory alloys under a

rapid heating pulse, Experimental Mechanics, Vol. 50, No. 7(2010), pp. 803-811.

[5] B. Selden, K. J. Cho and H. H., Asada, Multi-segment state coordination for

reducing latency time of shape memory alloy actuator systems, Proceedings of the

2005 IEEE International Conference on Robotics and Automation, (2005), pp.

1350-1355.

[6] K. George and I. Mayo, "Memory Metal." Chem Matters, Vol. 4, No. 7(1993).

[7] B. Kiefer and D. C. Lagoudas, Magnetic field-induced martensitic variant

reorientation in magnetic shape memory alloys, Philosophical Magazine, Vol. 85,

No. 33-35(2005), pp. 4285-4329.

[8] I. Karaman, B. Basaran, H. E. Karaca, A. I. Karsilayan and Y. I. Chumlyakov,

Energy harvesting using martensite variant reorientation mechanism in NiMnGa

magnetic shape memory alloy, Applied physics letters, Vol. 90, No. 17(2007), pp.

172505-172505-3.

[9] H. Yu, Y. Kang, Z. Zhao, X. Wang and L. Chen, Microstructural characteristics and

texture of hot strip low carbon steel produced by flexible thin slab rolling with

warm rolling technology, Materials Characterization, Vol. 56, No. 2(2006), pp.

158-164.

[10] J. Yanagimoto and R. Izumi, Continuous electric resistance heating: hot forming

system for high-alloy metals with poor workability. Journal of Materials

http://en.wikipedia.org/wiki/Robotics

http://www.sciencedirect.com/science/journal/09244247

http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=202



http://link.springer.com/search?facet-author=%22Roy+Featherstone%22

http://link.springer.com/search?facet-author=%22Yee+Harn+Teh%22

http://link.springer.com/book/10.1007/11552246

http://link.springer.com/search?facet-author=%22S.+Vollach%22

http://link.springer.com/search?facet-author=%22D.+Shilo%22

http://link.springer.com/journal/11340

http://ieeexplore.ieee.org/search/searchresult.jsp?searchWithin=p_Authors:.QT.Selden,%20B..QT.&searchWithin=p_Author_Ids:37564277100&newsearch=true

http://ieeexplore.ieee.org/search/searchresult.jsp?searchWithin=p_Authors:.QT.Cho,%20K.-J..QT.&searchWithin=p_Author_Ids:37279028900&newsearch=true

http://ieeexplore.ieee.org/search/searchresult.jsp?searchWithin=p_Authors:.QT.Asada,%20H.H..QT.&searchWithin=p_Author_Ids:37279023100&newsearch=true





http://scitation.aip.org/content/contributor/AU0393408;jsessionid=234b6imicf7j5.x-aip-live-06





http://www.sciencedirect.com/science/article/pii/S1044580305002391





REFERENCES

150

Processing Technology, Vol. 209, No. 6(2009), pp. 3060-3068.

[11] V. Brailovski, S. Prokoshkin, I. Khemelevskaya, K. Inaekyan, V. Demers, S.

Dobatkin and E. Tatyanin., Structure and properties of the Ti-50.0 % at Ni alloy

after strain hardening and nanocrystallizing thermomechanical processing,

Materials Transactions, Vol. 47, No. 3(2006), pp. 795-804.

[12] S. D. Prokoshkin, I. Yu. Khmelevskaya, S. V. Dobatkin, I. B. Trubitsyna, E. V.

Tatyanin, V. V. Stolyarov, E. A. Prokofiev, Alloy composition, deformation

temperature, pressure and post-deformation annealing effects in severely deformed

Ti–Ni based shape memory alloys. Acta Materialia, Vol. 53, No. 9(2005), pp.

2703-2714

[13] K. Ikuta, M. Tsukamoto, and S. Hirose, Mathematical model and experimental

verification of shape memory alloy for designing micro actuator, Proc. IEEE Micro

Electro Mechanical Systems (Piscataway, NJ: IEEE), (1991), pp. 103-108.

[14] J. D. Harrison, Measurable changes concomitant with the shape memory effect

transformation, Engineering Aspects of Shape Memory Alloys,

Butterworth-Heinemann, (1990), pp. 106-111.

[15] A. Nagasawa, K. Enami, Y. Ishino, Y. Abe, S. Nenno, Reversible shape memory

effect, Scripta Metallurgica, Vol. 8, No. 9(1974), pp. 1055-1060.

[16] T. Saburi and S. Nenno, Reversible shape memory in Cu-Zn-Ga, Scripta

Metallurgica, Vol. 8, No.12 (1974), pp. 1363-1367.

[17] V. Brailovski, S. Prokoshkin, P. Terriault, and F. Trochu, Shape memory Alloys:

Fundamentals, Modeling and Applications, University of Quebec higher institute of

technology, (2003).

[18] T. V. Duerig, K.N. Melton, D. Stockel and C. M. Wayman, Engineering aspects of

shape memory alloys, Chapter 1, Butterworth-Heinemann, (1990).

[19] K. Ikuta, Micro/miniature shape memory alloy actuator. In IEEE Robotics and

Automation Society, Vol. 3(1990), pp. 2156-2161.

[20] Toki Corporation, Tokyo- Japan, Biometal GlLidebook, (1987).

[21] K. Ikuta, M. Tsukamoto and S. Hirose, Proc. IEEE MEMS Workshop (1991) 108.

[22] O. K. Rediniotis, L. N. Wilson, D. C. Lagoudas and M. M. Khan, Development of a

shape-memory-alloy actuated biomimetic hydrofoil. Journal of Intelligent Material

Systems and Structures, Vol. 13, No. 1(2002), pp. 35-49.

http://www.sciencedirect.com/science/article/pii/S135964540500131X






REFERENCES

151

[23] A. David Johnson, V. Martynov, V. Gupta, Applications of shape memory alloys:

advantages, disadvantages, and limitations, Micromachining and Microfabrication,

International Society for Optics and Photonics, (2001), pp. 341-351.

[24] S. Suresh, Fatigue of Materials, Cambridge solid state science series, Cambridge

University Press, Cambridge, (1991).

[25] H. J. Christ, Wechselverformung von Metallen, Werkstoff-Forschung und-Technik

9, Springer, Berlin, (1991).

[26] H. O. Fuchs and R. I. Stephens, Metal Fatigue in Engineering, Wiley, New York,

(1980).

[27] J. J. Craig, Introduction to robotics: mechanics and control. Addison-Wesley

Publishing Group, 2nd edition, (1989).

[28] C. Liang and C.A. Rogers, Design of shape memory alloy actuators, J.intell.Mater.

Syst. &Struct, Vol. 6, No. 2(1995), pp. 220-338.

[29] K. Kuribayashi, A new actuator of a joint mechanism using Ti-Ni alloy wire. The

International Journal of Robotics Research, Vol. 4, No. 4(1986), pp. 47-58.

[30] K. Tanaka, A thermomechanical sketch of shape memory effect: One-dimensional

tensile behavior, Res Mechanica, International Journal of Structural Mechanics

and Materials Science, Vol. 18(1986), pp. 251-263.

[31] H. E. Mohammad and A. Hashem, Nonlinear control of a shape memory alloy

actuated manipulator, Journal of vibration and acoustics, Vol. 124, No. 4(2002), pp.

566-575.

[32] K. Tanaka and S. Nagaki, Thermomechanical description of materials with internal

variables in the process of phase transitions, Ingenieur-Archive, Vol. 51, No.

5(1982), pp. 287-299.

[33] J. G. Boyd and D. C. Lagoudas, A thermodynamic constitutive model for the shape

memory materials. Part I: the monolithic shape memory alloys, International

Journal of Plasticity, Vol. 12, No. 6(1996), pp. 805-842.

[34] C. Liang and C. A. Rogers, One-dimensional thermomechanical constitutive

relations for shape memory materials, Journal of Intelligent Material Systems and

Structures, Vol. 1, No. 2(1990), pp. 207-234.

[35] C. A. Rogers, C. Liang and C. R. Fuller, Modeling of shape memory alloy hybrid

composites for structural acoustic control, Journal of Acoustic Society of America,

http://profiles.spiedigitallibrary.org/summary.aspx?DOI=10.1117%2f12.442964&Name=A.+David+Johnson

http://profiles.spiedigitallibrary.org/summary.aspx?DOI=10.1117%2f12.442964&Name=Valery+Martynov

http://profiles.spiedigitallibrary.org/summary.aspx?DOI=10.1117%2f12.442964&Name=Vikas+Gupta

REFERENCES

152

Vol. 89 No. 1(1991), pp. 210-220.

[36] W. S. Anders, C. A. Rogers, C. Liang and C. R. Fuller, Vibration and low-frequency

acoustic analysis of piecewise-activated adaptive composite panels, Journal of

Composite Materials, Vol. 26, No. 1(1992), pp. 103-120.

[37] D. Grant, Accurate and rapid control of shape memory alloy actuators. PhD thesis,

McGill University, (1999).

[38] S. M. Dutta and F. H. Ghorbel, Differential hysteresis modeling of a shape memory

alloy wire actuator, IEEE/ASME Transactions on Mechatronics Vol. 10, No.

2(2005), pp. 189-197.

[39] A. Visintin, Differential models of hysteresis. Berlin, Germany, Springer-Verlag,

(1994).

[40] J. Kopfová and P. Pavel Krejcí, A Preisach type model for temperature driven

hysteresis memory erasure in shape memory materials, Continuum Mechanics and

Thermodynamics, Vol. 23, No. 2(2011), pp. 125-137.

[41] R. Gorbet, D. Wang and K. Morris, Preisach model identification of a two-wire

SMA actuator, in Proceedings of IEEE International Conference on Robotics and

Automation, Vol. 3(1998), pp. 2161-2167.

[42] W. Galinaitis and R. Rogers, Compensation for hysteresis using bivariate Preisach

models. In SPIE Smart Structures and Materials, Vol. 3039(1997), pp. 538-547.

[43] O. Henze and W. M. Rucker, Identification procedures of Preisach model, IEEE

Trans. Magn., Vol. 38, No. 2(2002), pp. 833-836.

[44] E. Cardelli, E. D. Torre and G. Ban, Experimental determination of Preisach

distribution functions in magnetic cores, Phys. B: Cond. Matter, Vol. 275, No.

1(2000), pp. 262 -269.

[45] C. Natale, F. Velardi and C. Visone, Identification and compensation of Preisach

hysteresis models for magnetostrictive actuators, Phys.B:Cond.Matter, Vol. 306,

No. 1(2001), pp. 161-165.

[46] M. Ruderman and T. Bertram, Discrete dynamic Preisach model for robust inverse

control of hysteresis systems, Decision and Control (CDC), 2010 49th IEEE

Conference on. IEEE, (2010), pp. 3463-3468.

[47] R. Smith, Inverse compensation for hysteresis magnetostrictive transducers,

Mathematical and Computer Modelling, Vol. 33, No. 1(2001), pp. 285-298.

http://link.springer.com/search?facet-author=%22Jana+Kopfov%C3%A1%22

http://link.springer.com/search?facet-author=%22Pavel+Krejc%CC%86%C3%AD%22



REFERENCES

153

[48] S. Bashash and N. Jalili, Robust multiple frequency trajectory tracking control of

piezoelectrically driven micro/nanopositioning systems, IEEE Trans Control Syst

Technol, Vol. 15, No. 5(2007), pp. 867-878.

[49] P. Krejci, Hysteresis, convexity and dissipation in hyperbolic equations,

Gakkotosho, Tokyo, (1996).

[50] P. Krejci and K. Kuhnen, Inverse control of systems with hysteresis and creep,

Proc. Inst. Elect. Eng.-Control Theory Appl., Vol. 148, No. 3(2001), pp. 185-192.

[51] X. Chen and T. Hisayama, Adaptive sliding-mode position control for

piezo-actuated stage, IEEE Trans. Ind. Electron., Vol. 55, No. 11(2008), pp.

3927-3934.

[52] K. Kuhnen, Modeling, Identification and compensation of complex hysteretic

nonlinearities, Eur. J. Control, Vol. 9(2003), pp. 407-418.

[53] M. Brokate and J. Sprekels, Hysteresis and phase transitions, Springer, New York,

(1996).

[54] A. Visintin, Differential models of hysteresis, Springer, Berlin, (1994).

[55] P. Krejci and K. Kuhnen, Inverse control of systems with hysteresis and creep,

IEEE Proc Control Theory Appl, Vol. 148, No. 3(2001), pp. 185-192.

[56] P. Ge and M. Jouaneh, Tracking control of a piezoceramic actuator, IEEE Trans.

Control Syst. Technol., Vol. 4, No. 3(1996), pp. 209-216.

[57] J. Nealis and R. C. Smith, Model-based robust control design for magnetostrictive

transducers operating in hysteretic and nonlinear regimes, IEEE Trans. Control

Syst. Technol., Vol. 15, No. 1(2007), pp. 22-39.

[58] C. Ru, L. Chen, B. Shao, W. Rong and L. Sun, A hysteresis compensation method

of piezoelectric actuator: model, identification and control, Control Eng Pract, Vol.

17, (2009), pp. 1107-1114.

[59] X. Tan and J. S. Baras, Adaptive Identification and Control of Hysteresis in Smart

Materials, IEEE Transactions on Automatic Control, Vol. 50, No. 6(2005), pp.

827-839.

[60] G. Song, J. Zhao, X. Zhou and J. Abreu-Garcia, Tracking control of a piezoceramic

actuator with hysteresis compensation using inverse Preisach model, IEEE/ASME

Trans. Mechatronics, Vol. 10, No. 2(2005), pp. 198-209.

[61] M. A. Janaideh, S. Rakheja and C. Y. Su, An analytical generalized

REFERENCES

154

Prandtl-Ishlinskii model inversion for hysteresis compensation in micropositioning

control, IEEE/ASME Trans Mech, Vol. 16, No. 4(2011), pp. 734-744.

[62] S. Hassan and R. Z. Mohammad, Position control of shape memory alloy

actuator based on the generalized Prandtl-Ishlinskii inverse model, Mechatronics,

Vol. 22, No. 7(2012), pp. 945-957.

[63] E. Asua, V. Etxebarria and A. Garcia-Arribas, Micropositioning control using shape

memory alloys, In: Proceedings of IEEE conference on control applications

CCA2006, Munich, Germany, (2006), pp. 3229-3234.

[64] E. P. Da Silva, Beam shape feedback control by means of a shape memory actuator,

Materials & design, Vol. 28, No. 5(2007), pp. 1592-1596.

[65] A.V. Popov, M. Labib, J. Fays and R. M. Botez, Closed-loop control simulations on

a morphing wing, Journal of Aircraft, Vol. 45, No. 5(2008), pp. 1794-1803.

[66] E. Shameli, A. Alasty and H. Salaarieh, Stability analysis and nonlinearity control

of a miniature shape memory alloy actuator for precise applications, Mechatronics,

Vol. 15, No. 4(2005), pp. 471-486.

[67] K. Ahn and B. Nguyen, Position control of shape memory alloy actuators using

self-tuning fuzzy PID controller, Int J Control, Automat, Syst, Vol. 4, No. 6(2006),

pp. 756-762.

[68] J. Carvajal, G. Chen and H. Ogmen, Fuzzy PID controller: design, performance

evaluation, and stability analysis, Inform Sci, Vol. 123, No. 3(2000), pp. 249-270.

[69] H. Li and H. Gatland, A new methodology for designing a fuzzy logic controller,

IEEE Transactions on, Vol. 25, No. 3(1995), pp.505-512.

[70] C. Cocaud, A. Price, A. Jnifene and H. Naguib, Position control of an experimental

robotic arm driven by artificial muscles based on shape memory alloys,

International Journal of Mechanics and Materials in Design, Vol. 3, No. 3(2006),

pp. 223-236.

[71] N. Ma and G. Song, Control of shape memory alloy actuator using pulse width

modulation, Smart Mater. Struct., Vol. 12, No. 5(2003), pp. 712-719.

[72] N. Ma and G. Song, Control of shape memory alloy actuators using pulse-width

pulse-frequency (PWPF), J Intell Mater Syst Struct, Vol. 14, No. 1(2003), pp.

15-22.

[73] J. Ko, M. B. Jun, G. Gilardi, E. Haslam and E. J. Park, Fuzzy PWM-PID control of




http://www.sciencedirect.com/science/journal/09574158/22/7




REFERENCES

155

cocontracting antagonistic shape memory alloy muscle pairs in an artificial finger,

Mechatronics, Vol. 21, No. 7(2011), pp. 1190-1202.

[74] D. Grant and V. Hayward, Variable structure control of shape memory alloy

actuators, IEEE Control Syst Mag, Vol. 17, No. 3(1997), pp. 80-88.

[75] J. Jayender, R.V. Patel, S. Nikumb, M. Ostojic, Modelling and gain scheduled

control of shape memory alloy actuators, Control Applications, 2005. CCA 2005.

Proceedings of 2005 IEEE Conference on. IEEE, (2005), pp. 767-772.

[76] A. Kumagai, P. Hozian and M. Kirkland, Neuro-fuzzy model based feedback

controller for shape memory alloy actuators, Proc. SPIE, (2000), pp. 291-299.

[77] G. Song, V. Chaudhry and C. Batur, Precision tracking control of shape memory

alloy actuators using neural networks and a sliding-mode based robust controller,

Smart Materials and Structures, Vol. 12, No. 2(2003), pp. 223-231.

[78] G. V. Webb and D. C. Lagoudas, Hysteresis modeling of SMA actuators for control

application, Journal of Intelligent Material Systems and Structures, Vol. 9, No.

6(1998), pp. 432-448.

[79] G. Webb, L. Wilson, D. Lagoudas, and O. Rediniotis, Adaptive control of shape

memory alloy actuators for underwater biomimetic applications, AIAA journal, Vol.

38, No. 2(2000), pp. 325-334.

[80] Y. H. Teh and R. Featherstone, An architecture for fast and accurate control of

shape memory alloy actuators, Int. J. Robotics Research, Vol. 27, No.5(2008),

pp.595-611.

[81] B. Selden, K. J. Cho and H. H. Asada, Segmented shape memory alloy actuators

using hysteresis loop control, Smart Mater Struct, Vol. 15, No. 2(2006), pp.

624-625..

[82] T. Hasegawa and S. Majima, A control system to compensate the hysteresis by

Preisach model on SMA actuator, Proceedings of the 1998 International

Symposium on Micromechatronics and Human Science, (1998), pp. 171-176.

[83] C. C. Lan, Investigation on pre-tensioned shape memory alloy actuators for force

and displacement self-sensing, in Intelligent Robots and Systems (IROS), IEEE/RSJ

International Conference, Taiwan, (2010), pp. 3043-3048.

[84] E. Asua, J. Feutchwanger, A. García-Arribas, V. Etxebarria, Sensorless control of

SMA-based actuators using neural networks, Journal of Intelligent Material


http://ieeexplore.ieee.org/search/searchresult.jsp?searchWithin=p_Authors:.QT.Jayender,%20J..QT.&searchWithin=p_Author_Ids:37299635700&newsearch=true

http://ieeexplore.ieee.org/search/searchresult.jsp?searchWithin=p_Authors:.QT.Jayender,%20J..QT.&searchWithin=p_Author_Ids:37299635700&newsearch=true

http://ieeexplore.ieee.org/search/searchresult.jsp?searchWithin=p_Authors:.QT.Nikumb,%20S..QT.&searchWithin=p_Author_Ids:37284795000&newsearch=true

http://ieeexplore.ieee.org/search/searchresult.jsp?searchWithin=p_Authors:.QT.Ostojic,%20M..QT.&searchWithin=p_Author_Ids:37283196600&newsearch=true

http://ieeexplore.ieee.org/search/searchresult.jsp?searchWithin=p_Authors:.QT.Hasegawa,%20T..QT.&searchWithin=p_Author_Ids:37335352600&newsearch=true

http://ieeexplore.ieee.org/search/searchresult.jsp?searchWithin=p_Authors:.QT.Majima,%20S..QT.&searchWithin=p_Author_Ids:37297421200&newsearch=true

http://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnumber=745777&queryText%3Dsumiko+majima+resistance

http://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnumber=745777&queryText%3Dsumiko+majima+resistance





http://jim.sagepub.com/search?author1=Estibalitz+Asua&sortspec=date&submit=Submit

http://jim.sagepub.com/search?author1=Jorge+Feutchwanger&sortspec=date&submit=Submit

http://jim.sagepub.com/search?author1=Alfredo+Garc%C3%ADa-Arribas&sortspec=date&submit=Submit

http://jim.sagepub.com/search?author1=Victor+Etxebarria&sortspec=date&submit=Submit

REFERENCES

156

Systems and Structures [J. Intellig. Mater. Syst. Struct.], Vol. 21, No. 18(2010), pp.

1809-1818.

[85] N. Ma, G. Song and H. Lee, Position control of shape memory alloy actuators with

internal electrical resistance feedback using neural networks, Smart Mater. Struct.,

Vol. 13,No. 4(2004), pp. 777-783.

[86] S. Hirose, K. Ikuta and Y. Umetani, A new design method of servo-actuators based

on the shape memory effect, Proc. of 5th RO.MAN.SY.symp. (1984); pp. 339-349.

[87] E. Williams and H. E. Mohammad, An Automotive SMA mirror actuator: modeling,

design, and experimental evaluation, Journal of Intelligent Material Systems and

Structures, Vol. 19, No. 12(2008), pp.1425-1434.

Documents

Phase Resistance Feedback Control and … for use Title Phase Resistance Feedback Control and Modeling of Thick SMA Actuators Author(s) 李, 軍鋒 Citation 北海道大学. 博士(工学)